LMFDB - Embedded newform 140.2.o.a.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	140.31
Dual form			140.2.o.a.131.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0915727 - 1.41125i) q^{2} +(1.49907 - 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +O(q^{10})$	\(q+(0.0915727 - 1.41125i) q^{2} +(1.49907 - 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(0.626319 + 1.26796i) q^{10} +(1.93693 + 1.11828i) q^{11} +(-3.64409 + 4.76194i) q^{12} +3.17109i q^{13} +(2.52997 - 2.75667i) q^{14} +2.99814i q^{15} +(3.86639 + 1.02518i) q^{16} +(-2.98390 - 1.72275i) q^{17} +(-7.59365 + 3.75094i) q^{18} +(-1.02618 - 1.77739i) q^{19} +(1.84676 - 0.767779i) q^{20} +(7.39711 - 2.86441i) q^{21} +(1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(6.38656 + 5.57878i) q^{24} +(0.500000 - 0.866025i) q^{25} +(4.47519 + 0.290385i) q^{26} -8.96105 q^{27} +(-3.65867 - 3.82285i) q^{28} -7.38092 q^{29} +(4.23112 + 0.274548i) q^{30} +(2.44599 - 4.23658i) q^{31} +(1.80084 - 5.36255i) q^{32} +(5.80718 - 3.35278i) q^{33} +(-2.70447 + 4.05325i) q^{34} +(-2.61438 - 0.406219i) q^{35} +(4.59812 + 11.0600i) q^{36} +(5.59689 + 9.69410i) q^{37} +(-2.60230 + 1.28543i) q^{38} +(8.23364 + 4.75369i) q^{39} +(-0.914412 - 2.67654i) q^{40} +1.46011i q^{41} +(-3.36501 - 10.7014i) q^{42} +9.95752i q^{43} +(-3.55233 - 2.71844i) q^{44} +(5.18651 + 2.99443i) q^{45} +(-1.66686 - 3.37451i) q^{46} +(-3.06343 - 5.30601i) q^{47} +(8.45786 - 8.50215i) q^{48} +(1.49553 + 6.83838i) q^{49} +(-1.17639 - 0.784927i) q^{50} +(-8.94615 + 5.16506i) q^{51} +(0.819610 - 6.28900i) q^{52} +(-2.32888 + 4.03374i) q^{53} +(-0.820587 + 12.6462i) q^{54} -2.23657 q^{55} +(-5.73001 + 4.81321i) q^{56} -6.15325 q^{57} +(-0.675891 + 10.4163i) q^{58} +(3.55938 - 6.16503i) q^{59} +(0.774910 - 5.94600i) q^{60} +(-2.19681 + 1.26833i) q^{61} +(-5.75488 - 3.83985i) q^{62} +(2.43279 - 15.6572i) q^{63} +(-7.40297 - 3.03249i) q^{64} +(-1.58555 - 2.74625i) q^{65} +(-4.19981 - 8.50238i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(5.47248 + 4.18784i) q^{68} -7.97917i q^{69} +(-0.812681 + 3.65233i) q^{70} +0.212347i q^{71} +(16.0294 - 5.47629i) q^{72} +(-12.8816 - 7.43720i) q^{73} +(14.1933 - 7.01088i) q^{74} +(-1.49907 - 2.59647i) q^{75} +(1.57575 + 3.79020i) q^{76} +(2.13680 + 5.51813i) q^{77} +(7.46261 - 11.1844i) q^{78} +(-0.399413 + 0.230601i) q^{79} +(-3.86099 + 1.04536i) q^{80} +(-4.44995 + 7.70755i) q^{81} +(2.06058 + 0.133707i) q^{82} -10.9174 q^{83} +(-15.4105 + 3.76890i) q^{84} +3.44551 q^{85} +(14.0525 + 0.911837i) q^{86} +(-11.0645 + 19.1643i) q^{87} +(-4.16168 + 4.76428i) q^{88} +(6.07992 - 3.51024i) q^{89} +(4.70082 - 7.04523i) q^{90} +(-5.26080 + 6.53565i) q^{91} +(-4.91490 + 2.04334i) q^{92} +(-7.33344 - 12.7019i) q^{93} +(-7.76862 + 3.83736i) q^{94} +(1.77739 + 1.02618i) q^{95} +(-11.2241 - 12.7147i) q^{96} -0.185459i q^{97} +(9.78758 - 1.48435i) q^{98} -13.3945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0915727	−	1.41125i	0.0647517	−	0.997901i
$2$	0.0915727	−	1.41125i	0.0647517	−	0.997901i
$3$	1.49907	−	2.59647i	0.865490	−	1.49907i	−0.00107081	−	0.999999i	$-0.500341\pi$
$3$	1.49907	−	2.59647i	0.865490	−	1.49907i	0.866560	−	0.499072i	$-0.166326\pi$
$4$	−1.98323	−	0.258463i	−0.991614	−	0.129232i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−3.52698	−	2.35332i	−1.43988	−	0.960741i
$7$	2.06101	+	1.65899i	0.778989	+	0.627038i
$7$	2.06101	+	1.65899i	0.778989	+	0.627038i
$8$	−0.546365	+	2.77516i	−0.193169	+	0.981165i
$9$	−2.99443	−	5.18651i	−0.998144	−	1.72884i
$10$	0.626319	+	1.26796i	0.198059	+	0.400964i
$11$	1.93693	+	1.11828i	0.584005	+	0.337175i	0.762723	−	0.646725i	$-0.223862\pi$
$11$	1.93693	+	1.11828i	0.584005	+	0.337175i	−0.178718	+	0.983900i	$0.557195\pi$
$12$	−3.64409	+	4.76194i	−1.05196	+	1.37465i
$13$			3.17109i			0.879502i	0.898120	+	0.439751i	$0.144933\pi$
$13$			3.17109i			0.879502i	−0.898120	+	0.439751i	$0.855067\pi$
$14$	2.52997	−	2.75667i	0.676163	−	0.736752i
$15$			2.99814i			0.774117i
$16$	3.86639	+	1.02518i	0.966598	+	0.256296i
$17$	−2.98390	−	1.72275i	−0.723701	−	0.417829i	0.0924124	−	0.995721i	$-0.470542\pi$
$17$	−2.98390	−	1.72275i	−0.723701	−	0.417829i	−0.816113	+	0.577892i	$0.803876\pi$
$18$	−7.59365	+	3.75094i	−1.78984	+	0.884104i
$19$	−1.02618	−	1.77739i	−0.235421	−	0.407761i	0.723974	−	0.689827i	$-0.242314\pi$
$19$	−1.02618	−	1.77739i	−0.235421	−	0.407761i	−0.959395	+	0.282066i	$0.908980\pi$
$20$	1.84676	−	0.767779i	0.412948	−	0.171681i
$21$	7.39711	−	2.86441i	1.61418	−	0.625065i
$22$	1.75554	−	2.63107i	0.374283	−	0.560947i
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	−0.240074	−	0.970755i	$-0.577172\pi$
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	0.720661	+	0.693288i	$0.243838\pi$
$24$	6.38656	+	5.57878i	1.30365	+	1.13876i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	4.47519	+	0.290385i	0.877657	+	0.0569493i
$27$	−8.96105			−1.72455
$28$	−3.65867	−	3.82285i	−0.691423	−	0.722450i
$29$	−7.38092			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$29$	−7.38092			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$30$	4.23112	+	0.274548i	0.772493	+	0.0501254i
$31$	2.44599	−	4.23658i	0.439313	−	0.760913i	−0.558323	−	0.829623i	$-0.688555\pi$
$31$	2.44599	−	4.23658i	0.439313	−	0.760913i	0.997637	+	0.0687104i	$0.0218884\pi$
$32$	1.80084	−	5.36255i	0.318347	−	0.947974i
$33$	5.80718	−	3.35278i	1.01090	−	0.583643i
$34$	−2.70447	+	4.05325i	−0.463813	+	0.695127i
$35$	−2.61438	−	0.406219i	−0.441911	−	0.0686636i
$36$	4.59812	+	11.0600i	0.766354	+	1.84333i
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.799222	+	0.601036i	$0.205245\pi$
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.120902	+	0.992664i	$0.461421\pi$
$38$	−2.60230	+	1.28543i	−0.422149	+	0.208524i
$39$	8.23364	+	4.75369i	1.31844	+	0.761200i
$40$	−0.914412	−	2.67654i	−0.144581	−	0.423198i
$41$			1.46011i			0.228031i	0.993479	+	0.114016i	$0.0363714\pi$
$41$			1.46011i			0.228031i	−0.993479	+	0.114016i	$0.963629\pi$
$42$	−3.36501	−	10.7014i	−0.519233	−	1.65127i
$43$			9.95752i			1.51851i	0.650794	+	0.759254i	$0.274436\pi$
$43$			9.95752i			1.51851i	−0.650794	+	0.759254i	$0.725564\pi$
$44$	−3.55233	−	2.71844i	−0.535534	−	0.409820i
$45$	5.18651	+	2.99443i	0.773159	+	0.446384i
$46$	−1.66686	−	3.37451i	−0.245766	−	0.497545i
$47$	−3.06343	−	5.30601i	−0.446847	−	0.773962i	0.551332	−	0.834286i	$-0.314120\pi$
$47$	−3.06343	−	5.30601i	−0.446847	−	0.773962i	−0.998179	+	0.0603243i	$0.980787\pi$
$48$	8.45786	−	8.50215i	1.22079	−	1.22718i
$49$	1.49553	+	6.83838i	0.213647	+	0.976911i
$50$	−1.17639	−	0.784927i	−0.166366	−	0.111005i
$51$	−8.94615	+	5.16506i	−1.25271	+	0.723253i
$52$	0.819610	−	6.28900i	0.113659	−	0.872127i
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	−0.980466	−	0.196688i	$-0.936982\pi$
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	0.660570	+	0.750765i	$0.270315\pi$
$54$	−0.820587	+	12.6462i	−0.111668	+	1.72094i
$55$	−2.23657			−0.301579
$56$	−5.73001	+	4.81321i	−0.765705	+	0.643193i
$57$	−6.15325			−0.815018
$58$	−0.675891	+	10.4163i	−0.0887488	+	1.36773i
$59$	3.55938	−	6.16503i	0.463392	−	0.802619i	−0.535735	−	0.844386i	$-0.679965\pi$
$59$	3.55938	−	6.16503i	0.463392	−	0.802619i	0.999127	+	0.0417674i	$0.0132988\pi$
$60$	0.774910	−	5.94600i	0.100040	−	0.767626i
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	−0.633999	−	0.773334i	$-0.718588\pi$
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	0.352727	+	0.935726i	$0.385254\pi$
$62$	−5.75488	−	3.83985i	−0.730870	−	0.487662i
$63$	2.43279	−	15.6572i	0.306503	−	1.97262i
$64$	−7.40297	−	3.03249i	−0.925371	−	0.379062i
$65$	−1.58555	−	2.74625i	−0.196663	−	0.340630i
$66$	−4.19981	−	8.50238i	−0.516961	−	1.04657i
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	0.502789	−	0.864409i	$-0.332307\pi$
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	−0.497206	+	0.867633i	$0.665641\pi$
$68$	5.47248	+	4.18784i	0.663636	+	0.507850i
$69$		−	7.97917i		−	0.960579i
$70$	−0.812681	+	3.65233i	−0.0971340	+	0.436538i
$71$			0.212347i			0.0252009i	0.999921	+	0.0126005i	$0.00401095\pi$
$71$			0.212347i			0.0252009i	−0.999921	+	0.0126005i	$0.995989\pi$
$72$	16.0294	−	5.47629i	1.88909	−	0.645387i
$73$	−12.8816	−	7.43720i	−1.50768	−	0.870459i	−0.999960	−	0.00893589i	$-0.997156\pi$
$73$	−12.8816	−	7.43720i	−1.50768	−	0.870459i	−0.507719	−	0.861523i	$-0.669511\pi$
$74$	14.1933	−	7.01088i	1.64994	−	0.814998i
$75$	−1.49907	−	2.59647i	−0.173098	−	0.299814i
$76$	1.57575	+	3.79020i	0.180751	+	0.434766i
$77$	2.13680	+	5.51813i	0.243511	+	0.628849i
$78$	7.46261	−	11.1844i	0.844974	−	1.26638i
$79$	−0.399413	+	0.230601i	−0.0449375	+	0.0259447i	−0.522300	−	0.852762i	$-0.674926\pi$
$79$	−0.399413	+	0.230601i	−0.0449375	+	0.0259447i	0.477363	+	0.878706i	$0.341593\pi$
$80$	−3.86099	+	1.04536i	−0.431671	+	0.116875i
$81$	−4.44995	+	7.70755i	−0.494439	+	0.856394i
$82$	2.06058	+	0.133707i	0.227553	+	0.0147654i
$83$	−10.9174			−1.19834			−0.599168	−	0.800624i	$-0.704502\pi$
$83$	−10.9174			−1.19834			−0.599168	+	0.800624i	$0.704502\pi$
$84$	−15.4105	+	3.76890i	−1.68142	+	0.411221i
$85$	3.44551			0.373718
$86$	14.0525	+	0.911837i	1.51532	+	0.0983259i
$87$	−11.0645	+	19.1643i	−1.18624	+	2.05463i
$88$	−4.16168	+	4.76428i	−0.443637	+	0.507874i
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	−0.141864	−	0.989886i	$-0.545310\pi$
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	0.786334	+	0.617801i	$0.211976\pi$
$90$	4.70082	−	7.04523i	0.495510	−	0.742633i
$91$	−5.26080	+	6.53565i	−0.551481	+	0.685122i
$92$	−4.91490	+	2.04334i	−0.512414	+	0.213033i
$93$	−7.33344	−	12.7019i	−0.760442	−	1.31712i
$94$	−7.76862	+	3.83736i	−0.801272	+	0.395794i
$95$	1.77739	+	1.02618i	0.182356	+	0.105284i
$96$	−11.2241	−	12.7147i	−1.14556	−	1.29769i
$97$		−	0.185459i		−	0.0188305i	−0.999956	−	0.00941523i	$-0.997003\pi$
$97$		−	0.185459i		−	0.0188305i	0.999956	−	0.00941523i	$-0.00299701\pi$
$98$	9.78758	−	1.48435i	0.988695	−	0.149942i
$99$		−	13.3945i		−	1.34620i
$100$	−1.21545	+	1.58830i	−0.121545	+	0.158830i
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	0.205979	−	0.978556i	$-0.433962\pi$
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	−0.744465	+	0.667661i	$0.767295\pi$
$102$	6.46995	+	13.0982i	0.640620	+	1.29691i
$103$	5.70918	+	9.88858i	0.562542	+	0.974351i	0.997274	+	0.0737911i	$0.0235098\pi$
$103$	5.70918	+	9.88858i	0.562542	+	0.974351i	−0.434732	+	0.900560i	$0.643157\pi$
$104$	−8.80027	−	1.73257i	−0.862937	−	0.169893i
$105$	−4.97388	+	6.17921i	−0.485401	+	0.603029i
$106$	5.47934	+	3.65601i	0.532201	+	0.355103i
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	−0.605024	−	0.796207i	$-0.706837\pi$
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	0.387023	+	0.922070i	$0.373503\pi$
$108$	17.7718	+	2.31610i	1.71009	+	0.222867i
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	−0.889019	−	0.457871i	$-0.848612\pi$
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	0.841037	+	0.540978i	$0.181946\pi$
$110$	−0.204809	+	3.15635i	−0.0195277	+	0.300946i
$111$	33.5606			3.18543
$112$	6.26791	+	8.52721i	0.592262	+	0.805745i
$113$	14.8588			1.39780			0.698899	−	0.715220i	$-0.253674\pi$
$113$	14.8588			1.39780			0.698899	+	0.715220i	$0.253674\pi$
$114$	−0.563470	+	8.68375i	−0.0527738	+	0.813307i
$115$	−1.33068	+	2.30481i	−0.124087	+	0.214925i
$116$	14.6381	+	1.90770i	1.35911	+	0.177125i
$117$	16.4469	−	9.49562i	1.52052	−	0.877870i
$118$	−8.37443	−	5.58771i	−0.770929	−	0.514391i
$119$	−3.29182	−	8.50085i	−0.301760	−	0.779272i
$120$	−8.32031	−	1.63808i	−0.759537	−	0.149536i
$121$	−2.99888	−	5.19421i	−0.272626	−	0.472201i
$122$	1.58875	+	3.21638i	0.143839	+	0.291197i
$123$	3.79114	+	2.18882i	0.341836	+	0.197359i
$124$	−5.94597	+	7.76992i	−0.533963	+	0.697759i
$125$			1.00000i			0.0894427i
$126$	−21.8733	−	4.86704i	−1.94863	−	0.433590i
$127$		−	3.02360i		−	0.268301i	−0.990961	−	0.134151i	$-0.957169\pi$
$127$		−	3.02360i		−	0.268301i	0.990961	−	0.134151i	$-0.0428306\pi$
$128$	−4.95750	+	10.1697i	−0.438186	+	0.898885i
$129$	25.8544	+	14.9270i	2.27635	+	1.31425i
$130$	−4.02082	+	1.98611i	−0.352649	+	0.174194i
$131$	−7.85267	−	13.6012i	−0.686091	−	1.18834i	−0.973093	−	0.230414i	$-0.925992\pi$
$131$	−7.85267	−	13.6012i	−0.686091	−	1.18834i	0.287002	−	0.957930i	$-0.407341\pi$
$132$	−12.3835	+	5.14838i	−1.07785	+	0.448109i
$133$	0.833705	−	5.36563i	0.0722914	−	0.465259i
$134$	0.0414202	−	0.0620775i	0.00357816	−	0.00536268i
$135$	7.76049	−	4.48052i	0.667917	−	0.385622i
$136$	6.41120	−	7.33952i	0.549756	−	0.629359i
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	−0.994967	−	0.100203i	$-0.968051\pi$
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	0.584262	+	0.811565i	$0.301384\pi$
$138$	−11.2606	−	0.730674i	−0.958563	−	0.0621991i
$139$	7.49745			0.635925			0.317963	−	0.948103i	$-0.397001\pi$
$139$	7.49745			0.635925			0.317963	+	0.948103i	$0.397001\pi$
$140$	5.07992	+	1.48135i	0.429332	+	0.125197i
$141$	−18.3692			−1.54697
$142$	0.299673	+	0.0194451i	0.0251480	+	0.00163180i
$143$	−3.54618	+	6.14217i	−0.296547	+	0.513634i
$144$	−6.26053	−	23.1229i	−0.521711	−	1.92691i
$145$	6.39206	−	3.69046i	0.530832	−	0.306476i
$146$	−11.6753	+	17.4981i	−0.966257	+	1.44815i
$147$	19.9975	+	6.36813i	1.64937	+	0.525234i
$148$	−8.59435	−	20.6722i	−0.706451	−	1.69925i
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	0.701600	−	0.712571i	$-0.252469\pi$
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	−0.967905	+	0.251318i	$0.919136\pi$
$150$	−3.80153	+	1.87779i	−0.310394	+	0.153321i
$151$	−20.5029	−	11.8373i	−1.66850	−	0.963309i	−0.968448	−	0.249217i	$-0.919827\pi$
$151$	−20.5029	−	11.8373i	−1.66850	−	0.963309i	−0.700052	−	0.714092i	$-0.746840\pi$
$152$	5.49320	−	1.87670i	0.445557	−	0.152220i
$153$			20.6347i			1.66821i
$154$	7.98311	−	2.51025i	0.643297	−	0.202281i
$155$			4.89199i			0.392934i
$156$	−15.1005	−	11.5558i	−1.20901	−	0.925201i
$157$	6.78313	+	3.91624i	0.541353	+	0.312550i	0.745627	−	0.666363i	$-0.232150\pi$
$157$	6.78313	+	3.91624i	0.541353	+	0.312550i	−0.204274	+	0.978914i	$0.565483\pi$
$158$	0.288860	+	0.584787i	0.0229805	+	0.0465232i
$159$	6.98233	+	12.0937i	0.553734	+	0.959096i
$160$	1.12170	+	5.54453i	0.0886783	+	0.438333i
$161$	6.95783	+	1.08110i	0.548354	+	0.0852026i
$162$	10.4697	+	6.98578i	0.822581	+	0.548855i
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	−0.0845574	−	0.996419i	$-0.526948\pi$
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	0.820645	+	0.571438i	$0.193614\pi$
$164$	0.377386	−	2.89574i	0.0294689	−	0.226119i
$165$	−3.35278	+	5.80718i	−0.261013	+	0.452088i
$166$	−0.999731	+	15.4071i	−0.0775942	+	1.19582i
$167$	11.7476			0.909058			0.454529	−	0.890732i	$-0.349808\pi$
$167$	11.7476			0.909058			0.454529	+	0.890732i	$0.349808\pi$
$168$	3.90766	+	22.0931i	0.301483	+	1.70452i
$169$	2.94418			0.226476
$170$	0.315514	−	4.86246i	0.0241988	−	0.372933i
$171$	−6.14563	+	10.6445i	−0.469968	+	0.814009i
$172$	2.57365	−	19.7480i	0.196239	−	1.50577i
$173$	−14.2785	+	8.24371i	−1.08558	+	0.626758i	−0.932395	−	0.361440i	$-0.882285\pi$
$173$	−14.2785	+	8.24371i	−1.08558	+	0.626758i	−0.153181	+	0.988198i	$0.548952\pi$
$174$	26.0324	+	17.3697i	1.97351	+	1.31679i
$175$	2.46723	−	0.955394i	0.186505	−	0.0722210i
$176$	6.34247	+	6.30943i	0.478082	+	0.475591i
$177$	−10.6715	−	18.4836i	−0.802122	−	1.38932i
$178$	−4.39706	−	8.90170i	−0.329574	−	0.667211i
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	0.764964	−	0.644073i	$-0.222757\pi$
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	−0.175302	+	0.984515i	$0.556090\pi$
$180$	−9.51208	−	7.27917i	−0.708989	−	0.542557i
$181$		−	16.5755i		−	1.23205i	−0.787728	−	0.616023i	$-0.788743\pi$
$181$		−	16.5755i		−	1.23205i	0.787728	−	0.616023i	$-0.211257\pi$
$182$	8.74166	+	8.02276i	0.647975	+	0.594687i
$183$			7.60525i			0.562196i
$184$	2.43359	+	7.12325i	0.179406	+	0.525133i
$185$	−9.69410	−	5.59689i	−0.712725	−	0.411492i
$186$	−18.5970	+	9.18614i	−1.36360	+	0.673560i
$187$	−3.85305	−	6.67369i	−0.281763	−	0.488028i
$188$	4.70407	+	11.3148i	0.343080	+	0.825218i
$189$	−18.4688	−	14.8663i	−1.34341	−	1.08136i
$190$	1.61095	−	2.41436i	0.116870	−	0.175156i
$191$	2.59197	−	1.49648i	0.187549	−	0.108281i	−0.403286	−	0.915074i	$-0.632132\pi$
$191$	2.59197	−	1.49648i	0.187549	−	0.108281i	0.590834	+	0.806793i	$0.298799\pi$
$192$	−18.9714	+	14.6757i	−1.36914	+	1.05912i
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	−0.470030	−	0.882651i	$-0.655757\pi$
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	0.999413	−	0.0342676i	$-0.0109098\pi$
$194$	−0.261728	−	0.0169829i	−0.0187909	−	0.00121930i
$195$	−9.50739			−0.680838
$196$	−1.19851	−	13.9486i	−0.0856075	−	0.996329i
$197$	4.81748			0.343231			0.171616	−	0.985164i	$-0.445101\pi$
$197$	4.81748			0.343231			0.171616	+	0.985164i	$0.445101\pi$
$198$	−18.9029	−	1.22657i	−1.34337	−	0.0871686i
$199$	0.637180	−	1.10363i	0.0451685	−	0.0782342i	−0.842557	−	0.538607i	$-0.818951\pi$
$199$	0.637180	−	1.10363i	0.0451685	−	0.0782342i	0.887726	+	0.460373i	$0.152284\pi$
$200$	2.13017	+	1.86074i	0.150626	+	0.131574i
$201$	0.137014	−	0.0791053i	0.00966425	−	0.00557966i
$202$	−4.90494	+	7.35115i	−0.345110	+	0.517225i
$203$	−15.2122	−	12.2448i	−1.06768	−	0.859420i
$204$	19.0772	−	7.93125i	1.33567	−	0.555298i
$205$	−0.730057	−	1.26450i	−0.0509894	−	0.0883162i
$206$	14.4780	−	7.15153i	1.00873	−	0.498270i
$207$	−13.8032	−	7.96929i	−0.959390	−	0.553904i
$208$	−3.25095	+	12.2607i	−0.225413	+	0.850126i
$209$		−	4.59023i		−	0.317513i
$210$	8.26491	+	7.58521i	0.570333	+	0.523429i
$211$		−	3.70986i		−	0.255397i	−0.991813	−	0.127698i	$-0.959241\pi$
$211$		−	3.70986i		−	0.255397i	0.991813	−	0.127698i	$-0.0407590\pi$
$212$	5.66128	−	7.39791i	0.388818	−	0.508090i
$213$	0.551351	+	0.318323i	0.0377780	+	0.0218111i
$214$	1.63085	+	3.30161i	0.111483	+	0.225693i
$215$	−4.97876	−	8.62347i	−0.339549	−	0.588116i
$216$	4.89600	−	24.8683i	0.333131	−	1.69207i
$217$	12.0697	−	4.67378i	0.819342	−	0.317277i
$218$	1.17861	+	0.786412i	0.0798258	+	0.0532625i
$219$	−38.6209	+	22.2978i	−2.60976	+	1.50675i
$220$	4.43563	+	0.578071i	0.299050	+	0.0389735i
$221$	5.46301	−	9.46220i	0.367482	−	0.636497i
$222$	3.07323	−	47.3622i	0.206262	−	3.17874i
$223$	12.9581			0.867737			0.433869	−	0.900976i	$-0.357148\pi$
$223$	12.9581			0.867737			0.433869	+	0.900976i	$0.357148\pi$
$224$	12.6080	−	8.06471i	0.842404	−	0.538846i
$225$	−5.98886			−0.399258
$226$	1.36066	−	20.9694i	0.0905098	−	1.39487i
$227$	4.44626	−	7.70115i	0.295109	−	0.511143i	−0.679901	−	0.733304i	$-0.737977\pi$
$227$	4.44626	−	7.70115i	0.295109	−	0.511143i	0.975010	+	0.222160i	$0.0713108\pi$
$228$	12.2033	+	1.59039i	0.808183	+	0.105326i
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	−0.822384	−	0.568933i	$-0.807357\pi$
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	0.0815180	+	0.996672i	$0.474023\pi$
$230$	3.13080	+	2.08898i	0.206439	+	0.137743i
$231$	17.5309	+	2.72392i	1.15345	+	0.179221i
$232$	4.03267	−	20.4832i	0.264758	−	1.34479i
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	0.999998	−	0.00182020i	$-0.000579387\pi$
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	−0.501576	+	0.865114i	$0.667246\pi$
$234$	−11.8946	−	24.0801i	−0.777572	−	1.57417i
$235$	5.30601	+	3.06343i	0.346126	+	0.199836i
$236$	−8.65250	+	11.3067i	−0.563230	+	0.736003i
$237$			1.38275i			0.0898194i
$238$	−12.2982	+	3.86712i	−0.797176	+	0.250668i
$239$			0.0438513i			0.00283650i	0.999999	+	0.00141825i	$0.000451444\pi$
$239$			0.0438513i			0.00283650i	−0.999999	+	0.00141825i	$0.999549\pi$
$240$	−3.07365	+	11.5920i	−0.198403	+	0.748261i
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	0.562795	−	0.826596i	$-0.309726\pi$
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	−0.434456	+	0.900693i	$0.643059\pi$
$242$	−7.60493	+	3.75651i	−0.488863	+	0.241478i
$243$	−0.0999675	−	0.173149i	−0.00641292	−	0.0111075i
$244$	4.68458	−	1.94759i	0.299900	−	0.124682i
$245$	−4.71435	−	5.17444i	−0.301189	−	0.330583i
$246$	3.43612	−	5.14979i	0.219079	−	0.328339i
$247$	5.63627	−	3.25410i	0.358627	−	0.207053i
$248$	10.4208	+	9.10273i	0.661720	+	0.578024i
$249$	−16.3659	+	28.3466i	−1.03715	+	1.79639i
$250$	1.41125	+	0.0915727i	0.0892550	+	0.00579157i
$251$	−6.32409			−0.399173			−0.199587	−	0.979880i	$-0.563960\pi$
$251$	−6.32409			−0.399173			−0.199587	+	0.979880i	$0.563960\pi$
$252$	−8.87159	+	30.4230i	−0.558857	+	1.91647i
$253$	5.95233			0.374220
$254$	−4.26704	−	0.276879i	−0.267738	−	0.0173729i
$255$	5.16506	−	8.94615i	0.323449	−	0.560229i
$256$	13.8980	+	7.92752i	0.868625	+	0.495470i
$257$	−12.3334	+	7.12068i	−0.769335	+	0.444176i	−0.832637	−	0.553819i	$-0.813170\pi$
$257$	−12.3334	+	7.12068i	−0.769335	+	0.444176i	0.0633025	+	0.997994i	$0.479837\pi$
$258$	23.4333	−	35.1200i	1.45889	−	2.18648i
$259$	−4.54713	+	29.2648i	−0.282545	+	1.81843i
$260$	2.43470	+	5.85624i	0.150993	+	0.363188i
$261$	22.1017	+	38.2812i	1.36806	+	2.36955i
$262$	−19.9138	+	9.83654i	−1.23028	+	0.607704i
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	0.152355	−	0.988326i	$-0.451314\pi$
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	−0.779738	+	0.626107i	$0.784647\pi$
$264$	6.13164	+	17.9477i	0.377376	+	1.10460i
$265$		−	4.65777i		−	0.286124i
$266$	−7.49588	−	1.66791i	−0.459602	−	0.102266i
$267$		−	21.0484i		−	1.28814i
$268$	−0.0838136	−	0.0641387i	−0.00511973	−	0.00391790i
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	0.258837	−	0.965921i	$-0.416661\pi$
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	−0.707094	+	0.707120i	$0.749994\pi$
$270$	−5.61247	−	11.3623i	−0.341564	−	0.691485i
$271$	3.98686	+	6.90544i	0.242184	+	0.419476i	0.961336	−	0.275377i	$-0.0888028\pi$
$271$	3.98686	+	6.90544i	0.242184	+	0.419476i	−0.719152	+	0.694853i	$0.755469\pi$
$272$	−9.77078	−	9.71988i	−0.592440	−	0.589354i
$273$	9.08330	+	23.4569i	0.549746	+	1.41968i
$274$	11.3102	+	7.54657i	0.683275	+	0.455905i
$275$	1.93693	−	1.11828i	0.116801	−	0.0674351i
$276$	−2.06232	+	15.8245i	−0.124137	+	0.952524i
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	−0.586289	−	0.810102i	$-0.699412\pi$
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	0.994713	+	0.102690i	$0.0327449\pi$
$278$	0.686562	−	10.5807i	0.0411772	−	0.634591i
$279$	−29.2974			−1.75399
$280$	2.55573	−	7.03337i	0.152734	−	0.420324i
$281$	9.48286			0.565700			0.282850	−	0.959164i	$-0.408720\pi$
$281$	9.48286			0.565700			0.282850	+	0.959164i	$0.408720\pi$
$282$	−1.68212	+	25.9235i	−0.100169	+	1.54372i
$283$	10.7746	−	18.6621i	0.640483	−	1.10935i	−0.344842	−	0.938661i	$-0.612067\pi$
$283$	10.7746	−	18.6621i	0.640483	−	1.10935i	0.985325	−	0.170689i	$-0.0545993\pi$
$284$	0.0548838	−	0.421132i	0.00325675	−	0.0249896i
$285$	5.32887	−	3.07662i	0.315655	−	0.182244i
$286$	8.34337	+	5.56699i	0.493354	+	0.329183i
$287$	−2.42231	+	3.00931i	−0.142984	+	0.177634i
$288$	−33.2054	+	6.71772i	−1.95665	+	0.395845i
$289$	−2.56424	−	4.44140i	−0.150838	−	0.261259i
$290$	−4.62281	−	9.35872i	−0.271461	−	0.549563i
$291$	−0.481537	−	0.278016i	−0.0282282	−	0.0162976i
$292$	23.6249	+	18.0791i	1.38255	+	1.05800i
$293$			28.9496i			1.69125i	0.533776	+	0.845626i	$0.320773\pi$
$293$			28.9496i			1.69125i	−0.533776	+	0.845626i	$0.679227\pi$
$294$	10.8182	−	27.6383i	0.630931	−	1.61190i
$295$			7.11876i			0.414470i
$296$	−29.9606	+	10.2357i	−1.74142	+	0.594940i
$297$	−17.3569	−	10.0210i	−1.00715	−	0.581477i
$298$	−8.24342	+	4.07190i	−0.477529	+	0.235879i
$299$	4.21972	+	7.30877i	0.244033	+	0.422677i
$300$	2.30191	+	5.53685i	0.132901	+	0.319670i
$301$	−16.5194	+	20.5226i	−0.952162	+	1.18290i
$302$	−18.5829	+	27.8506i	−1.06933	+	1.60262i
$303$	−16.2251	+	9.36757i	−0.932108	+	0.538153i
$304$	−2.14545	−	7.92411i	−0.123050	−	0.454479i
$305$	1.26833	−	2.19681i	0.0726242	−	0.125789i
$306$	29.1206	+	1.88957i	1.66471	+	0.108020i
$307$	8.00589			0.456920			0.228460	−	0.973553i	$-0.426631\pi$
$307$	8.00589			0.456920			0.228460	+	0.973553i	$0.426631\pi$
$308$	−2.81154	−	11.4960i	−0.160202	−	0.655045i
$309$	34.2339			1.94750
$310$	6.90379	+	0.447972i	0.392109	+	0.0254431i
$311$	−6.87633	+	11.9101i	−0.389921	+	0.675363i	−0.992438	−	0.122743i	$-0.960831\pi$
$311$	−6.87633	+	11.9101i	−0.389921	+	0.675363i	0.602518	+	0.798105i	$0.294164\pi$
$312$	−17.6908	+	20.2524i	−1.00154	+	1.14656i
$313$	9.21091	−	5.31792i	0.520631	−	0.300587i	−0.216562	−	0.976269i	$-0.569484\pi$
$313$	9.21091	−	5.31792i	0.520631	−	0.300587i	0.737193	+	0.675682i	$0.236151\pi$
$314$	6.14793	−	9.21404i	0.346948	−	0.519979i
$315$	5.72173	+	14.7759i	0.322383	+	0.832528i
$316$	0.851730	−	0.354102i	0.0479136	−	0.0199198i
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	0.999651	−	0.0264211i	$-0.00841107\pi$
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	−0.522707	+	0.852513i	$0.675078\pi$
$318$	17.7066	−	8.74632i	0.992939	−	0.490469i
$319$	−14.2963	−	8.25397i	−0.800439	−	0.462133i
$320$	7.92741	−	1.07527i	0.443156	−	0.0601094i
$321$			7.80679i			0.435732i
$322$	2.16284	−	9.72021i	0.120531	−	0.541686i
$323$			7.07140i			0.393463i
$324$	10.8174	−	14.1357i	0.600966	−	0.785316i
$325$	2.74625	+	1.58555i	0.152334	+	0.0879502i
$326$	−6.79654	−	13.7594i	−0.376426	−	0.762061i
$327$	1.50191	+	2.60138i	0.0830557	+	0.143857i
$328$	−4.05204	−	0.797755i	−0.223737	−	0.0440486i
$329$	2.48885	−	16.0179i	0.137215	−	0.883097i
$330$	7.88833	+	5.26337i	0.434239	+	0.289739i
$331$	−7.21415	+	4.16509i	−0.396525	+	0.228934i	−0.684984	−	0.728558i	$-0.740191\pi$
$331$	−7.21415	+	4.16509i	−0.396525	+	0.228934i	0.288458	+	0.957492i	$0.406857\pi$
$332$	21.6516	+	2.82173i	1.18829	+	0.154863i
$333$	33.5190	−	58.0567i	1.83683	−	3.18149i
$334$	1.07576	−	16.5788i	0.0588630	−	0.907150i
$335$	−0.0527695			−0.00288311
$336$	31.5367	−	3.49154i	1.72047	−	0.190479i
$337$	−27.0772			−1.47499			−0.737495	−	0.675353i	$-0.763991\pi$
$337$	−27.0772			−1.47499			−0.737495	+	0.675353i	$0.763991\pi$
$338$	0.269607	−	4.15496i	0.0146647	−	0.226000i
$339$	22.2744	−	38.5804i	1.20978	−	2.09540i
$340$	−6.83323	−	0.890536i	−0.370584	−	0.0482961i
$341$	9.47541	−	5.47063i	0.513122	−	0.296251i
$342$	14.4593	+	9.64775i	0.781870	+	0.521690i
$343$	−8.26248	+	16.5750i	−0.446132	+	0.894967i
$344$	−27.6337	−	5.44044i	−1.48991	−	0.293329i
$345$	3.98958	+	6.91016i	0.214792	+	0.372031i
$346$	10.3264	+	20.9054i	0.555150	+	1.12388i
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.978857	−	0.204544i	$-0.0655713\pi$
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.312288	+	0.949987i	$0.398905\pi$
$348$	26.8968	−	35.1475i	1.44182	−	1.88410i
$349$			9.64063i			0.516051i	0.966138	+	0.258026i	$0.0830719\pi$
$349$			9.64063i			0.516051i	−0.966138	+	0.258026i	$0.916928\pi$
$350$	−1.12237	−	3.56936i	−0.0599929	−	0.190790i
$351$		−	28.4163i		−	1.51675i
$352$	9.48495	−	8.37301i	0.505550	−	0.446283i
$353$	−14.1283	−	8.15697i	−0.751973	−	0.434152i	0.0744333	−	0.997226i	$-0.476285\pi$
$353$	−14.1283	−	8.15697i	−0.751973	−	0.434152i	−0.826406	+	0.563074i	$0.809619\pi$
$354$	−27.0622	+	13.3676i	−1.43834	+	0.710478i
$355$	−0.106173	−	0.183898i	−0.00563509	−	0.00976027i
$356$	−12.9651	+	5.39018i	−0.687151	+	0.285679i
$357$	−27.0069	−	4.19629i	−1.42936	−	0.222091i
$358$	7.15037	−	10.7164i	0.377909	−	0.566380i
$359$	−1.38744	+	0.801040i	−0.0732264	+	0.0422773i	−0.536166	−	0.844112i	$-0.680128\pi$
$359$	−1.38744	+	0.801040i	−0.0732264	+	0.0422773i	0.462940	+	0.886390i	$0.346795\pi$
$360$	−11.1437	+	12.7573i	−0.587327	+	0.672370i
$361$	7.39392	−	12.8067i	0.389154	−	0.674034i
$362$	−23.3921	−	1.51786i	−1.22946	−	0.0797771i
$363$	−17.9822			−0.943818
$364$	12.1226	−	11.6020i	0.635396	−	0.608108i
$365$	14.8744			0.778562
$366$	10.7329	+	0.696433i	0.561016	+	0.0364031i
$367$	0.630259	−	1.09164i	0.0328993	−	0.0569832i	−0.849107	−	0.528221i	$-0.822859\pi$
$367$	0.630259	−	1.09164i	0.0328993	−	0.0569832i	0.882006	+	0.471238i	$0.156193\pi$
$368$	10.2755	−	2.78209i	0.535648	−	0.145027i
$369$	7.57289	−	4.37221i	0.394229	−	0.227608i
$370$	−8.78631	+	13.1682i	−0.456778	+	0.684584i
$371$	−11.4918	+	4.45000i	−0.596623	+	0.231033i
$372$	11.2609	+	27.0862i	0.583851	+	1.40435i
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	0.721507	−	0.692408i	$-0.243450\pi$
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	−0.960396	+	0.278639i	$0.910117\pi$
$374$	−9.77105	+	4.82648i	−0.505249	+	0.249571i
$375$	2.59647	+	1.49907i	0.134081	+	0.0774117i
$376$	16.3988	−	5.60247i	0.845702	−	0.288925i
$377$		−	23.4056i		−	1.20545i
$378$	−22.6712	+	24.7027i	−1.16608	+	1.27057i
$379$		−	2.53516i		−	0.130223i	−0.997878	−	0.0651113i	$-0.979260\pi$
$379$		−	2.53516i		−	0.130223i	0.997878	−	0.0651113i	$-0.0207403\pi$
$380$	−3.25974	−	2.49453i	−0.167221	−	0.127967i
$381$	−7.85068	−	4.53259i	−0.402203	−	0.232212i
$382$	−1.87454	−	3.79495i	−0.0959099	−	0.194166i
$383$	0.662435	+	1.14737i	0.0338489	+	0.0586279i	0.882454	−	0.470400i	$-0.155890\pi$
$383$	0.662435	+	1.14737i	0.0338489	+	0.0586279i	−0.848605	+	0.529027i	$0.822557\pi$
$384$	18.9737	+	28.1171i	0.968248	+	1.43485i
$385$	−4.60959	−	3.71044i	−0.234926	−	0.189101i
$386$	−17.3033	−	11.5454i	−0.880715	−	0.587644i
$387$	51.6448	−	29.8171i	2.62525	−	1.51569i
$388$	−0.0479342	+	0.367807i	−0.00243349	+	0.0186726i
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	0.0909120	+	0.995859i	$0.471022\pi$
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	−0.907895	+	0.419197i	$0.862312\pi$
$390$	−0.870617	+	13.4173i	−0.0440854	+	0.679409i
$391$	−9.16976			−0.463735
$392$	−19.7947	+	0.414074i	−0.999781	+	0.0209139i
$393$	−47.0869			−2.37522
$394$	0.441150	−	6.79865i	0.0222248	−	0.342511i
$395$	0.230601	−	0.399413i	0.0116028	−	0.0200967i
$396$	−3.46199	+	26.5644i	−0.173971	+	1.33491i
$397$	−30.4617	+	17.5871i	−1.52883	+	0.882670i	−0.529419	+	0.848361i	$0.677590\pi$
$397$	−30.4617	+	17.5871i	−1.52883	+	0.882670i	−0.999411	+	0.0343095i	$0.989077\pi$
$398$	−1.49914	−	1.00028i	−0.0751452	−	0.0501395i
$399$	−12.6819	−	10.2082i	−0.634890	−	0.511047i
$400$	2.82103	−	2.83580i	0.141052	−	0.141790i
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	−0.921484	−	0.388416i	$-0.873022\pi$
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$402$	−0.0990903	−	0.200605i	−0.00494217	−	0.0100053i
$403$	13.4346	+	7.75647i	0.669225	+	0.386377i
$404$	9.92512	+	7.59524i	0.493793	+	0.377877i
$405$		−	8.89991i		−	0.442240i
$406$	−18.6735	+	20.3468i	−0.926751	+	1.00979i
$407$			25.0357i			1.24097i
$408$	−9.44599	−	27.6490i	−0.467646	−	1.36883i
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	0.808424	−	0.588600i	$-0.200321\pi$
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	−0.105530	+	0.994416i	$0.533654\pi$
$410$	−1.85137	+	0.914496i	−0.0914325	+	0.0451638i
$411$	14.4126	+	24.9634i	0.710922	+	1.23135i
$412$	−8.76677	−	21.0869i	−0.431908	−	1.03888i
$413$	17.5636	−	6.80123i	0.864250	−	0.334666i
$414$	−12.5106	+	18.7500i	−0.614864	+	0.921510i
$415$	9.45470	−	5.45868i	0.464113	−	0.267956i
$416$	17.0051	+	5.71063i	0.833746	+	0.279987i
$417$	11.2392	−	19.4669i	0.550387	−	0.953298i
$418$	−6.47794	−	0.420340i	−0.316846	−	0.0205595i
$419$	11.8654			0.579665			0.289832	−	0.957077i	$-0.406400\pi$
$419$	11.8654			0.579665			0.289832	+	0.957077i	$0.406400\pi$
$420$	11.4614	−	10.9692i	0.559261	−	0.535243i
$421$	10.3433			0.504101			0.252051	−	0.967714i	$-0.418895\pi$
$421$	10.3433			0.504101			0.252051	+	0.967714i	$0.418895\pi$
$422$	−5.23552	−	0.339721i	−0.254861	−	0.0165374i
$423$	−18.3465	+	31.7770i	−0.892035	+	1.54505i
$424$	−9.92185	−	8.66691i	−0.481847	−	0.420902i
$425$	−2.98390	+	1.72275i	−0.144740	+	0.0835658i
$426$	0.499720	−	0.748942i	0.0242115	−	0.0362864i
$427$	−6.63178	−	1.03044i	−0.320934	−	0.0498663i
$428$	4.80873	−	1.99920i	0.232439	−	0.0966349i
$429$	10.6320	+	18.4151i	0.513316	+	0.889089i
$430$	−12.6257	+	6.23658i	−0.608868	+	0.300755i
$431$	25.6838	+	14.8286i	1.23715	+	0.714267i	0.968510	−	0.248975i	$-0.0800937\pi$
$431$	25.6838	+	14.8286i	1.23715	+	0.714267i	0.268636	+	0.963242i	$0.413427\pi$
$432$	−34.6469	−	9.18671i	−1.66695	−	0.441996i
$433$		−	29.4107i		−	1.41339i	−0.707520	−	0.706693i	$-0.750186\pi$
$433$		−	29.4107i		−	1.41339i	0.707520	−	0.706693i	$-0.249814\pi$
$434$	−5.49059	−	17.4612i	−0.263557	−	0.838166i
$435$		−	22.1291i		−	1.06101i
$436$	1.21775	−	1.59130i	0.0583196	−	0.0762094i
$437$	−4.73029	−	2.73103i	−0.226280	−	0.130643i
$438$	27.9311	+	56.5455i	1.33460	+	2.70185i
$439$	−4.41191	−	7.64165i	−0.210569	−	0.364716i	0.741324	−	0.671147i	$-0.234198\pi$
$439$	−4.41191	−	7.64165i	−0.210569	−	0.364716i	−0.951893	+	0.306432i	$0.900865\pi$
$440$	1.22198	−	6.20682i	0.0582557	−	0.295899i
$441$	30.9890	−	28.2336i	1.47567	−	1.34446i
$442$	−12.8532	−	8.57612i	−0.611366	−	0.407925i
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	−0.0401518	−	0.999194i	$-0.512784\pi$
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	0.845251	+	0.534369i	$0.179451\pi$
$444$	−66.5583	−	8.67417i	−3.15872	−	0.411658i
$445$	−3.51024	+	6.07992i	−0.166402	+	0.288216i
$446$	1.18661	−	18.2870i	0.0561874	−	0.865916i
$447$	−19.4919			−0.921935
$448$	−10.2267	−	18.5314i	−0.483168	−	0.875528i
$449$	5.02309			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$449$	5.02309			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$450$	−0.548417	+	8.45176i	−0.0258526	+	0.398420i
$451$	−1.63282	+	2.82813i	−0.0768866	+	0.133171i
$452$	−29.4684	−	3.84045i	−1.38608	−	0.180640i
$453$	−61.4705	+	35.4900i	−2.88814	+	1.66747i
$454$	−10.4611	−	6.97998i	−0.490962	−	0.327587i
$455$	1.28816	−	8.29044i	0.0603898	−	0.388662i
$456$	3.36192	−	17.0762i	0.157436	−	0.799667i
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	0.982816	+	0.184587i	$0.0590946\pi$
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	−0.331551	+	0.943437i	$0.607572\pi$
$458$	8.10816	+	16.4147i	0.378869	+	0.767008i
$459$	26.7388	+	15.4377i	1.24806	+	0.720569i
$460$	3.23476	−	4.22704i	0.150822	−	0.197087i
$461$			19.8494i			0.924481i	0.886755	+	0.462240i	$0.152954\pi$
$461$			19.8494i			0.924481i	−0.886755	+	0.462240i	$0.847046\pi$
$462$	5.44948	−	24.4909i	0.253533	−	1.13942i
$463$		−	35.7118i		−	1.65967i	−0.558012	−	0.829833i	$-0.688436\pi$
$463$		−	35.7118i		−	1.65967i	0.558012	−	0.829833i	$-0.311564\pi$
$464$	−28.5375	−	7.56680i	−1.32482	−	0.351280i
$465$	12.7019	+	7.33344i	0.589036	+	0.340080i
$466$	19.2935	−	9.53018i	0.893756	−	0.441477i
$467$	−11.3055	−	19.5818i	−0.523158	−	0.906136i	−0.999637	−	0.0269503i	$-0.991420\pi$
$467$	−11.3055	−	19.5818i	−0.523158	−	0.906136i	0.476479	−	0.879186i	$-0.341913\pi$
$468$	−35.0722	+	14.5811i	−1.62121	+	0.674010i
$469$	0.0504157	+	0.130195i	0.00232798	+	0.00601183i
$470$	4.80914	−	7.20756i	0.221829	−	0.332460i
$471$	20.3368	−	11.7415i	0.937070	−	0.541018i
$472$	15.1642	+	13.2462i	0.697989	+	0.609705i
$473$	−11.1353	+	19.2870i	−0.512003	+	0.886816i
$474$	1.95140	+	0.126622i	0.0896309	+	0.00581596i
$475$	−2.05235			−0.0941684
$476$	4.33127	+	17.7100i	0.198523	+	0.811734i
$477$	27.8947			1.27721
$478$	0.0618849	+	0.00401558i	0.00283055	+	0.000183668i
$479$	4.28200	−	7.41664i	0.195649	−	0.338875i	−0.751464	−	0.659774i	$-0.770652\pi$
$479$	4.28200	−	7.41664i	0.195649	−	0.338875i	0.947113	+	0.320900i	$0.103985\pi$
$480$	16.0777	+	5.39918i	0.733843	+	0.246438i
$481$	−30.7409	+	17.7483i	−1.40166	+	0.809251i
$482$	1.80579	−	2.70638i	0.0822515	−	0.123272i
$483$	13.2373	−	16.4451i	0.602319	−	0.748280i
$484$	4.60495	+	11.0764i	0.209316	+	0.503473i
$485$	0.0927293	+	0.160612i	0.00421062	+	0.00729301i
$486$	−0.253510	+	0.125223i	−0.0114994	+	0.00568023i
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.272386	−	0.962188i	$-0.587813\pi$
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.969472	+	0.245201i	$0.921146\pi$
$488$	−2.31955	−	6.78945i	−0.105001	−	0.307344i
$489$		−	32.5346i		−	1.47126i
$490$	−7.73412	+	6.17927i	−0.349392	+	0.279151i
$491$			35.7781i			1.61464i	0.590113	+	0.807321i	$0.299083\pi$
$491$			35.7781i			1.61464i	−0.590113	+	0.807321i	$0.700917\pi$
$492$	−6.95297	−	5.32079i	−0.313464	−	0.239880i
$493$	22.0239	+	12.7155i	0.991906	+	0.572677i
$494$	−4.07621	−	8.25214i	−0.183397	−	0.371281i
$495$	6.69725	+	11.6000i	0.301019	+	0.521380i
$496$	13.8004	−	13.8727i	0.619658	−	0.622903i
$497$	−0.352280	+	0.437649i	−0.0158019	+	0.0196312i
$498$	38.5053	+	25.6921i	1.72546	+	1.15129i
$499$	35.7797	−	20.6574i	1.60172	−	0.924752i	0.610574	−	0.791959i	$-0.290939\pi$
$499$	35.7797	−	20.6574i	1.60172	−	0.924752i	0.991144	−	0.132793i	$-0.0423947\pi$
$500$	0.258463	−	1.98323i	0.0115588	−	0.0886927i
$501$	17.6105	−	30.5023i	0.786780	−	1.36274i
$502$	−0.579114	+	8.92485i	−0.0258471	+	0.398336i
$503$	29.0170			1.29381			0.646903	−	0.762572i	$-0.276064\pi$
$503$	29.0170			1.29381			0.646903	+	0.762572i	$0.276064\pi$
$504$	42.1219	+	15.3059i	1.87626	+	0.681779i
$505$	6.24891			0.278073
$506$	0.545071	−	8.40021i	0.0242314	−	0.373435i
$507$	4.41354	−	7.64448i	0.196012	−	0.339503i
$508$	−0.781489	+	5.99649i	−0.0346730	+	0.266051i
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	−0.0635754	−	0.997977i	$-0.520250\pi$
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	0.832486	+	0.554046i	$0.186917\pi$
$510$	−12.1522	−	8.10839i	−0.538110	−	0.359046i
$511$	−14.2109	−	36.6986i	−0.628654	−	1.62345i
$512$	12.4604	−	18.8875i	0.550675	−	0.834720i
$513$	9.19562	+	15.9273i	0.405996	+	0.703206i
$514$	8.91962	+	18.0575i	0.393428	+	0.796481i
$515$	−9.88858	−	5.70918i	−0.435743	−	0.251576i
$516$	−47.4171	−	36.2861i	−2.08742	−	1.59741i
$517$		−	13.7031i		−	0.602663i
$518$	40.8835	+	9.09698i	1.79632	+	0.399698i
$519$			49.4317i			2.16981i
$520$	8.48754	−	2.89968i	0.372203	−	0.127160i
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	0.848211	−	0.529658i	$-0.177680\pi$
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	−0.0345917	+	0.999402i	$0.511013\pi$
$522$	56.0481	−	27.6854i	2.45316	−	1.21176i
$523$	20.5020	+	35.5105i	0.896491	+	1.55277i	0.831949	+	0.554852i	$0.187225\pi$
$523$	20.5020	+	35.5105i	0.896491	+	1.55277i	0.0645418	+	0.997915i	$0.479441\pi$
$524$	12.0582	+	29.0040i	0.526766	+	1.26704i
$525$	1.21790	−	7.83829i	0.0531537	−	0.342091i
$526$	−9.22165	+	13.8207i	−0.402083	+	0.602611i
$527$	−14.5972	+	8.42768i	−0.635863	+	0.367116i
$528$	25.8901	−	7.00973i	1.12672	−	0.305059i
$529$	−7.95856	+	13.7846i	−0.346024	+	0.599332i
$530$	−6.57325	−	0.426524i	−0.285524	−	0.0185270i
$531$	−42.6333			−1.85013
$532$	−3.04025	+	10.4258i	−0.131811	+	0.452016i
$533$	−4.63015			−0.200554
$534$	−29.7045	−	1.92746i	−1.28544	−	0.0834094i
$535$	1.30194	−	2.25502i	0.0562876	−	0.0974931i
$536$	−0.0981906	+	0.112408i	−0.00424119	+	0.00485530i
$537$	23.6528	−	13.6559i	1.02069	−	0.589297i
$538$	−6.66349	+	9.98673i	−0.287284	+	0.430559i
$539$	−4.75052	+	14.9178i	−0.204620	+	0.642557i
$540$	−16.5489	+	6.88010i	−0.712151	+	0.296072i
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	0.826524	−	0.562901i	$-0.190315\pi$
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	−0.900749	+	0.434341i	$0.856981\pi$
$542$	10.1104	−	4.99409i	0.434277	−	0.214514i
$543$	−43.0377	−	24.8479i	−1.84693	−	1.06632i
$544$	−14.6119	+	12.8989i	−0.626479	+	0.553035i
$545$		−	1.00189i		−	0.0429163i
$546$	33.9352	−	10.6708i	1.45229	−	0.456666i
$547$			28.2607i			1.20834i	0.796855	+	0.604170i	$0.206495\pi$
$547$			28.2607i			1.20834i	−0.796855	+	0.604170i	$0.793505\pi$
$548$	11.6858	−	15.2704i	0.499191	−	0.652321i
$549$	13.1564	+	7.59584i	0.561500	+	0.324182i
$550$	−1.40080	−	2.83588i	−0.0597305	−	0.120922i
$551$	7.57413	+	13.1188i	0.322669	+	0.558879i
$552$	22.1434	+	4.35953i	0.942487	+	0.185554i
$553$	−1.20576	−	0.187349i	−0.0512741	−	0.00796691i
$554$	−15.9931	−	10.6711i	−0.679481	−	0.453374i
$555$	−29.0643	+	16.7803i	−1.23371	+	0.712284i
$556$	−14.8692	−	1.93781i	−0.630593	−	0.0821816i
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	−0.887183	−	0.461417i	$-0.847341\pi$
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	0.843191	+	0.537615i	$0.180674\pi$
$558$	−2.68285	+	41.3459i	−0.113574	+	1.75031i
$559$	−31.5762			−1.33553
$560$	−9.69178	−	4.25082i	−0.409552	−	0.179630i
$561$	−23.1040			−0.975453
$562$	0.868371	−	13.3826i	0.0366300	−	0.564513i
$563$	−22.9547	+	39.7588i	−0.967426	+	1.67563i	−0.264477	+	0.964392i	$0.585199\pi$
$563$	−22.9547	+	39.7588i	−0.967426	+	1.67563i	−0.702949	+	0.711240i	$0.748134\pi$
$564$	36.4303	+	4.74776i	1.53399	+	0.199917i
$565$	−12.8681	+	7.42940i	−0.541365	+	0.312557i
$566$	−25.3502	−	16.9145i	−1.06555	−	0.710971i
$567$	−21.9581	+	8.50292i	−0.922154	+	0.357089i
$568$	−0.589295	−	0.116019i	−0.0247263	−	0.00486803i
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	0.770891	−	0.636968i	$-0.219811\pi$
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	−0.937075	+	0.349127i	$0.886478\pi$
$570$	−3.85389	−	7.80208i	−0.161422	−	0.326793i
$571$	−18.3314	−	10.5837i	−0.767147	−	0.442912i	0.0647092	−	0.997904i	$-0.479388\pi$
$571$	−18.3314	−	10.5837i	−0.767147	−	0.442912i	−0.831856	+	0.554992i	$0.812721\pi$
$572$	8.62041	−	11.2648i	0.360438	−	0.471003i
$573$		−	8.97330i		−	0.374865i
$574$	4.02506	+	3.69404i	0.168003	+	0.154186i
$575$		−	2.66137i		−	0.110987i
$576$	6.43964	+	47.4762i	0.268318	+	1.97817i
$577$	8.94731	+	5.16573i	0.372481	+	0.215052i	0.674542	−	0.738237i	$-0.264341\pi$
$577$	8.94731	+	5.16573i	0.372481	+	0.215052i	−0.302061	+	0.953289i	$0.597675\pi$
$578$	−6.50272	+	3.21207i	−0.270478	+	0.133604i
$579$	−22.0496	−	38.1911i	−0.916351	−	1.58717i
$580$	−13.6308	+	5.66691i	−0.565987	+	0.235306i
$581$	−22.5008	−	18.1117i	−0.933490	−	0.751402i
$582$	−0.436444	+	0.654109i	−0.0180912	+	0.0271137i
$583$	−9.02174	+	5.20871i	−0.373642	+	0.215723i
$584$	27.6774	−	31.6851i	1.14530	−	1.31114i
$585$	−9.49562	+	16.4469i	−0.392595	+	0.679995i
$586$	40.8550	+	2.65099i	1.68770	+	0.109511i
$587$	20.4660			0.844722			0.422361	−	0.906428i	$-0.361201\pi$
$587$	20.4660			0.844722			0.422361	+	0.906428i	$0.361201\pi$
$588$	−38.0138	−	17.7981i	−1.56766	−	0.733980i
$589$	−10.0401			−0.413694
$590$	10.0463	+	0.651884i	0.413601	+	0.0268377i
$591$	7.22175	−	12.5084i	0.297063	−	0.514529i
$592$	11.7016	+	43.2191i	0.480931	+	1.77629i
$593$	38.8389	−	22.4236i	1.59492	−	0.920828i	0.602477	−	0.798136i	$-0.294181\pi$
$593$	38.8389	−	22.4236i	1.59492	−	0.920828i	0.992445	−	0.122692i	$-0.0391527\pi$
$594$	−15.7315	+	23.5772i	−0.645471	+	0.967383i
$595$	7.10122	+	5.71605i	0.291122	+	0.234335i
$596$	4.99158	+	12.0064i	0.204463	+	0.491800i
$597$	−1.91036	−	3.30884i	−0.0781857	−	0.135422i
$598$	10.7009	−	5.28578i	0.437592	−	0.216152i
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	0.760397	−	0.649459i	$-0.225005\pi$
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	−0.182250	+	0.983252i	$0.558338\pi$
$600$	8.02464	−	2.74154i	0.327605	−	0.111923i
$601$			39.8029i			1.62359i	0.583941	+	0.811796i	$0.301510\pi$
$601$			39.8029i			1.62359i	−0.583941	+	0.811796i	$0.698490\pi$
$602$	27.4496	+	25.1922i	1.11876	+	1.02676i
$603$		−	0.316030i		−	0.0128697i
$604$	37.6024	+	28.7754i	1.53002	+	1.17085i
$605$	5.19421	+	2.99888i	0.211175	+	0.121922i
$606$	11.7342	+	23.7554i	0.476668	+	0.964998i
$607$	−4.70373	−	8.14710i	−0.190919	−	0.330681i	0.754636	−	0.656143i	$-0.227813\pi$
$607$	−4.70373	−	8.14710i	−0.190919	−	0.330681i	−0.945555	+	0.325463i	$0.894480\pi$
$608$	−11.3793	+	2.30213i	−0.461493	+	0.0933636i
$609$	−54.5975	+	21.1420i	−2.21240	+	0.856716i
$610$	−2.98409	−	1.99109i	−0.120822	−	0.0806168i
$611$	16.8259	−	9.71441i	0.680701	−	0.393003i
$612$	5.33330	−	40.9233i	0.215586	−	1.65423i
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	−0.970230	−	0.242187i	$-0.922135\pi$
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	0.694855	+	0.719150i	$0.255469\pi$
$614$	0.733121	−	11.2983i	0.0295863	−	0.455961i
$615$	−4.37763			−0.176523
$616$	−16.4811	+	2.91505i	−0.664044	+	0.117451i
$617$	39.1144			1.57469			0.787343	−	0.616515i	$-0.211456\pi$
$617$	39.1144			1.57469			0.787343	+	0.616515i	$0.211456\pi$
$618$	3.13489	−	48.3124i	0.126104	−	1.94341i
$619$	−9.50950	+	16.4709i	−0.382219	+	0.662023i	−0.991379	−	0.131024i	$-0.958173\pi$
$619$	−9.50950	+	16.4709i	−0.382219	+	0.662023i	0.609160	+	0.793047i	$0.291507\pi$
$620$	1.26440	−	9.70193i	0.0507795	−	0.389639i
$621$	−20.6535	+	11.9243i	−0.828798	+	0.478507i
$622$	16.1785	+	10.7948i	0.648697	+	0.432833i
$623$	18.3542	+	2.85186i	0.735347	+	0.114257i
$624$	26.9611	+	26.8206i	1.07931	+	1.07368i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.66143	−	13.4858i	−0.266244	−	0.539002i
$627$	−11.9184	−	6.88108i	−0.475974	−	0.274804i
$628$	−12.4403	−	9.52000i	−0.496422	−	0.379889i
$629$		−	38.5683i		−	1.53782i
$630$	21.3764	−	6.72169i	0.851656	−	0.267799i
$631$		−	16.4987i		−	0.656802i	−0.944538	−	0.328401i	$-0.893490\pi$
$631$		−	16.4987i		−	0.656802i	0.944538	−	0.328401i	$-0.106510\pi$
$632$	−0.421729	−	1.23443i	−0.0167755	−	0.0491028i
$633$	−9.63252	−	5.56134i	−0.382858	−	0.221043i
$634$	21.5344	−	10.6371i	0.855241	−	0.422452i
$635$	1.51180	+	2.61851i	0.0599939	+	0.103913i
$636$	−10.7218	−	25.7893i	−0.425146	−	1.02261i
$637$	−21.6851	+	4.74245i	−0.859196	+	0.187903i
$638$	−12.9575	+	19.4197i	−0.512993	+	0.768835i
$639$	1.10134	−	0.635857i	0.0435682	−	0.0251541i
$640$	−0.791535	−	11.2860i	−0.0312882	−	0.446118i
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	0.467173	+	0.884166i	$0.345272\pi$
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	−0.999297	+	0.0374991i	$0.988061\pi$
$642$	11.0173	+	0.714889i	0.434818	+	0.0282144i
$643$	43.6730			1.72229			0.861147	−	0.508355i	$-0.169746\pi$
$643$	43.6730			1.72229			0.861147	+	0.508355i	$0.169746\pi$
$644$	−13.5195	−	3.94241i	−0.532745	−	0.155353i
$645$	−29.8541			−1.17550
$646$	9.97948	+	0.647547i	0.392637	+	0.0254774i
$647$	−14.0540	+	24.3422i	−0.552518	+	0.956989i	0.445574	+	0.895245i	$0.353000\pi$
$647$	−14.0540	+	24.3422i	−0.552518	+	0.956989i	−0.998092	+	0.0617443i	$0.980334\pi$
$648$	−18.9583	−	16.5604i	−0.744754	−	0.650556i
$649$	13.7885	−	7.96080i	0.541246	−	0.312489i
$650$	2.48908	−	3.73043i	0.0976296	−	0.146320i
$651$	5.95797	−	38.3448i	0.233511	−	1.50285i
$652$	−20.0402	+	8.33161i	−0.784836	+	0.326291i
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	0.909038	+	0.416713i	$0.136818\pi$
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	−0.0936346	+	0.995607i	$0.529849\pi$
$654$	3.80872	−	1.88134i	0.148933	−	0.0735664i
$655$	13.6012	+	7.85267i	0.531444	+	0.306829i
$656$	−1.49688	+	5.64538i	−0.0584435	+	0.220415i
$657$			89.0808i			3.47537i
$658$	−22.3773	−	4.97918i	−0.872359	−	0.194109i
$659$		−	47.0951i		−	1.83457i	−0.398236	−	0.917283i	$-0.630378\pi$
$659$		−	47.0951i		−	1.83457i	0.398236	−	0.917283i	$-0.369622\pi$
$660$	8.15027	−	10.6504i	0.317249	−	0.414566i
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	0.291006	−	0.956721i	$-0.406010\pi$
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	−0.683042	+	0.730379i	$0.739343\pi$
$662$	5.21735	+	10.5623i	0.202778	+	0.410517i
$663$	−16.3789	−	28.3690i	−0.636103	−	1.10176i
$664$	5.96486	−	30.2973i	0.231481	−	1.17577i
$665$	1.96081	+	5.06363i	0.0760368	+	0.196359i
$666$	−78.8628	−	52.6200i	−3.05587	−	2.03898i
$667$	−17.0116	+	9.82168i	−0.658693	+	0.380297i
$668$	−23.2982	−	3.03633i	−0.901435	−	0.117479i
$669$	19.4251	−	33.6452i	0.751017	−	1.30080i
$670$	−0.00483225	+	0.0744708i	−0.000186686	+	0.00287706i
$671$	−5.67340			−0.219019
$672$	−2.03952	−	44.8257i	−0.0786763	−	1.72919i
$673$	14.9849			0.577626			0.288813	−	0.957385i	$-0.406739\pi$
$673$	14.9849			0.577626			0.288813	+	0.957385i	$0.406739\pi$
$674$	−2.47953	+	38.2126i	−0.0955080	+	1.47189i
$675$	−4.48052	+	7.76049i	−0.172455	+	0.298702i
$676$	−5.83899	−	0.760963i	−0.224576	−	0.0292678i
$677$	19.9347	−	11.5093i	0.766154	−	0.442339i	−0.0653470	−	0.997863i	$-0.520815\pi$
$677$	19.9347	−	11.5093i	0.766154	−	0.442339i	0.831501	+	0.555524i	$0.187482\pi$
$678$	−52.4067	−	34.9676i	−2.01267	−	1.34292i
$679$	0.307673	−	0.382232i	0.0118074	−	0.0146687i
$680$	−1.88250	+	9.56181i	−0.0721907	+	0.366679i
$681$	−13.3305	−	23.0892i	−0.510827	−	0.884779i
$682$	−6.85272	−	13.8731i	−0.262404	−	0.531228i
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.266945	−	0.963712i	$-0.586014\pi$
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.968071	+	0.250675i	$0.919348\pi$
$684$	14.9394	−	19.5222i	0.571223	−	0.746448i
$685$		−	9.61436i		−	0.367346i
$686$	22.6348	+	13.1782i	0.864201	+	0.503146i
$687$			38.8132i			1.48082i
$688$	−10.2083	+	38.4997i	−0.389187	+	1.46779i
$689$	−12.7914	−	7.38510i	−0.487312	−	0.281350i
$690$	10.1173	−	4.99750i	0.385158	−	0.190252i
$691$	13.9969	+	24.2433i	0.532467	+	0.922260i	0.999281	+	0.0379044i	$0.0120682\pi$
$691$	13.9969	+	24.2433i	0.532467	+	0.922260i	−0.466815	+	0.884355i	$0.654598\pi$
$692$	30.4483	−	12.6587i	1.15747	−	0.481211i
$693$	22.2213	−	27.6062i	0.844118	−	1.04867i
$694$	21.7991	−	32.6708i	0.827483	−	1.24017i
$695$	−6.49298	+	3.74872i	−0.246293	+	0.142197i
$696$	−47.1387	−	41.1765i	−1.78679	−	1.56079i
$697$	2.51542	−	4.35683i	0.0952782	−	0.165027i
$698$	13.6053	+	0.882819i	0.514968	+	0.0334152i
$699$	45.6203			1.72552
$700$	−5.14002	+	1.25708i	−0.194274	+	0.0475131i
$701$	29.2334			1.10413			0.552065	−	0.833801i	$-0.313840\pi$
$701$	29.2334			1.10413			0.552065	+	0.833801i	$0.313840\pi$
$702$	−40.1024	−	2.60216i	−1.51357	−	0.0982121i
$703$	11.4868	−	19.8957i	0.433233	−	0.750381i
$704$	−10.9478	−	14.1523i	−0.412611	−	0.533386i
$705$	15.9082	−	9.18460i	0.599137	−	0.345912i
$706$	−12.8053	+	19.1915i	−0.481932	+	0.722283i
$707$	−5.97017	−	15.4175i	−0.224532	−	0.579835i
$708$	16.3868	+	39.4155i	0.615852	+	1.48133i
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	0.902449	−	0.430796i	$-0.141767\pi$
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	−0.824305	+	0.566146i	$0.808434\pi$
$710$	−0.269247	+	0.132997i	−0.0101047	+	0.00499127i
$711$	2.39203	+	1.38104i	0.0897082	+	0.0517931i
$712$	6.41962	+	18.7906i	0.240585	+	0.704207i
$713$		−	13.0194i		−	0.487580i
$714$	−8.39509	+	37.7291i	−0.314178	+	1.41197i
$715$		−	7.09236i		−	0.265239i
$716$	−14.4687	−	11.0723i	−0.540722	−	0.413790i
$717$	0.113858	+	0.0657362i	0.00425212	+	0.00245496i
$718$	1.00341	+	2.03137i	0.0374470	+	0.0758102i
$719$	21.1113	+	36.5658i	0.787318	+	1.36368i	0.927604	+	0.373564i	$0.121865\pi$
$719$	21.1113	+	36.5658i	0.787318	+	1.36368i	−0.140286	+	0.990111i	$0.544802\pi$
$720$	16.9832	+	16.8948i	0.632928	+	0.629631i
$721$	−4.63835	+	29.8519i	−0.172741	+	1.11174i
$722$	−17.3962	−	11.6074i	−0.647421	−	0.431982i
$723$	5.97339	−	3.44874i	0.222153	−	0.128260i
$724$	−4.28415	+	32.8730i	−0.159219	+	1.22172i
$725$	−3.69046	+	6.39206i	−0.137060	+	0.237395i
$726$	−1.64667	+	25.3772i	−0.0611138	+	0.941837i
$727$	−27.2605			−1.01104			−0.505519	−	0.862816i	$-0.668699\pi$
$727$	−27.2605			−1.01104			−0.505519	+	0.862816i	$0.668699\pi$
$728$	−15.2631	−	18.1704i	−0.565689	−	0.673439i
$729$	−27.2992			−1.01108
$730$	1.36209	−	20.9914i	0.0504132	−	0.776928i
$731$	17.1544	−	29.7122i	0.634477	−	1.09895i
$732$	1.96568	−	15.0830i	0.0726535	−	0.557482i
$733$	13.2554	−	7.65300i	0.489599	−	0.282670i	−0.234809	−	0.972041i	$-0.575447\pi$
$733$	13.2554	−	7.65300i	0.489599	−	0.282670i	0.724408	+	0.689372i	$0.242113\pi$
$734$	−1.48286	−	0.989415i	−0.0547333	−	0.0365200i
$735$	−20.5024	+	4.48381i	−0.756244	+	0.165388i
$736$	−2.98526	−	14.7560i	−0.110038	−	0.543915i
$737$	0.0590113	+	0.102211i	0.00217371	+	0.00376498i
$738$	−5.47680	−	11.0876i	−0.201604	−	0.408140i
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.996635	−	0.0819692i	$-0.973879\pi$
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.569305	−	0.822126i	$-0.692788\pi$
$740$	17.7790	+	13.6055i	0.653570	+	0.500148i
$741$		−	19.5125i		−	0.716810i
$742$	5.22771	+	16.6252i	0.191915	+	0.610331i
$743$		−	35.2067i		−	1.29161i	−0.763503	−	0.645805i	$-0.776522\pi$
$743$		−	35.2067i		−	1.29161i	0.763503	−	0.645805i	$-0.223478\pi$
$744$	39.2564	−	13.4116i	1.43921	−	0.491692i
$745$	5.63031	+	3.25066i	0.206279	+	0.119095i
$746$	−11.7000	+	5.77932i	−0.428369	+	0.211596i
$747$	32.6913	+	56.6229i	1.19611	+	2.07173i
$748$	5.91659	+	14.2313i	0.216332	+	0.520349i
$749$	−6.80752	−	1.05774i	−0.248741	−	0.0386491i
$750$	2.35332	−	3.52698i	0.0859313	−	0.128787i
$751$	−0.584292	+	0.337341i	−0.0213211	+	0.0123098i	−0.510623	−	0.859805i	$-0.670585\pi$
$751$	−0.584292	+	0.337341i	−0.0213211	+	0.0123098i	0.489302	+	0.872115i	$0.337252\pi$
$752$	−6.40478	−	23.6557i	−0.233558	−	0.862635i
$753$	−9.48027	+	16.4203i	−0.345480	+	0.598389i
$754$	−33.0310	−	2.14331i	−1.20292	−	0.0780548i
$755$	23.6747			0.861609
$756$	32.7855	+	34.2567i	1.19240	+	1.24590i
$757$	−45.8640			−1.66695			−0.833477	−	0.552553i	$-0.813654\pi$
$757$	−45.8640			−1.66695			−0.833477	+	0.552553i	$0.813654\pi$
$758$	−3.57774	−	0.232152i	−0.129949	−	0.00843214i
$759$	8.92298	−	15.4550i	0.323883	−	0.560983i
$760$	−3.81890	+	4.37187i	−0.138526	+	0.158584i
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	−0.116139	−	0.993233i	$-0.537052\pi$
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	0.802095	+	0.597196i	$0.203719\pi$
$762$	−7.11551	+	10.6642i	−0.257768	+	0.386322i
$763$	−2.47190	+	0.957201i	−0.0894886	+	0.0346530i
$764$	−5.52726	+	2.29793i	−0.199969	+	0.0831360i
$765$	−10.3173	−	17.8701i	−0.373024	−	0.646097i
$766$	1.67988	−	0.829791i	0.0606967	−	0.0299816i
$767$	19.5499	+	11.2871i	0.705905	+	0.407554i
$768$	41.4177	−	24.2018i	1.49453	−	0.873307i
$769$		−	16.0214i		−	0.577745i	−0.957368	−	0.288872i	$-0.906720\pi$
$769$		−	16.0214i		−	0.577745i	0.957368	−	0.288872i	$-0.0932803\pi$
$770$	−5.65845	+	6.16549i	−0.203916	+	0.222189i
$771$			42.6976i			1.53772i
$772$	−17.8779	+	23.3620i	−0.643439	+	0.840816i
$773$	−36.6688	−	21.1707i	−1.31888	−	0.761458i	−0.335335	−	0.942099i	$-0.608850\pi$
$773$	−36.6688	−	21.1707i	−1.31888	−	0.761458i	−0.983549	+	0.180641i	$0.942183\pi$
$774$	−37.3500	−	75.6139i	−1.34252	−	2.71789i
$775$	−2.44599	−	4.23658i	−0.0878627	−	0.152183i
$776$	0.514676	+	0.101328i	0.0184758	+	0.00363746i
$777$	69.1687	+	55.6765i	2.48141	+	1.99738i
$778$	37.9113	+	25.2957i	1.35919	+	0.906896i
$779$	2.59519	−	1.49833i	0.0929824	−	0.0536834i
$780$	18.8553	+	2.45731i	0.675129	+	0.0879858i
$781$	−0.237464	+	0.411299i	−0.00849712	+	0.0147174i
$782$	−0.839700	+	12.9408i	−0.0300276	+	0.462762i
$783$	66.1408			2.36368
$784$	−1.22829	+	27.9730i	−0.0438675	+	0.999037i
$785$	−7.83249			−0.279553
$786$	−4.31187	+	66.4511i	−0.153799	+	2.37023i
$787$	2.19121	−	3.79528i	0.0781081	−	0.135287i	−0.824326	−	0.566116i	$-0.808445\pi$
$787$	2.19121	−	3.79528i	0.0781081	−	0.135287i	0.902434	+	0.430829i	$0.141779\pi$
$788$	−9.55417	−	1.24514i	−0.340353	−	0.0443563i
$789$	−30.5044	+	17.6117i	−1.08599	+	0.626994i
$790$	−0.542554	−	0.362011i	−0.0193032	−	0.0128798i
$791$	30.6241	+	24.6506i	1.08887	+	0.876473i
$792$	37.1718	+	7.31828i	1.32084	+	0.260044i
$793$	−4.02198	−	6.96627i	−0.142825	−	0.247380i
$794$	22.0302	+	44.5995i	0.781824	+	1.58278i
$795$	−12.0937	−	6.98233i	−0.428921	−	0.247638i
$796$	−1.54892	+	2.02406i	−0.0549001	+	0.0717409i
$797$		−	53.6019i		−	1.89868i	−0.314255	−	0.949339i	$-0.601755\pi$
$797$		−	53.6019i		−	1.89868i	0.314255	−	0.949339i	$-0.398245\pi$
$798$	−15.5675	+	16.9625i	−0.551085	+	0.600466i
$799$			21.1101i			0.746822i
$800$	−3.74369	−	4.24085i	−0.132359	−	0.149937i
$801$	−36.4118	−	21.0224i	−1.28655	−	0.742789i
$802$	−40.4792	+	19.9950i	−1.42937	+	0.706048i
$803$	−16.6338	−	28.8106i	−0.586995	−	1.01670i
$804$	−0.292177	+	0.121471i	−0.0103043	+	0.00428394i
$805$	−6.56621	+	2.54266i	−0.231428	+	0.0896169i
$806$	12.1765	−	18.2492i	0.428900	−	0.642802i
$807$	−22.0422	+	12.7261i	−0.775924	+	0.447980i
$808$	11.6276	−	13.3113i	0.409058	−	0.468289i
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	−0.852454	−	0.522803i	$-0.824886\pi$
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	0.878987	+	0.476845i	$0.158220\pi$
$810$	−12.5600	−	0.814989i	−0.441312	−	0.0286358i
$811$	−43.1894			−1.51658			−0.758292	−	0.651915i	$-0.773966\pi$
$811$	−43.1894			−1.51658			−0.758292	+	0.651915i	$0.773966\pi$
$812$	27.0043	+	28.2161i	0.947667	+	0.990192i
$813$	23.9063			0.838432
$814$	35.3315	+	2.29258i	1.23837	+	0.0803550i
$815$	−5.42579	+	9.39774i	−0.190057	+	0.329188i
$816$	−39.8845	+	10.7987i	−1.39624	+	0.378031i
$817$	17.6984	−	10.2182i	0.619189	−	0.357489i
$818$	12.8840	−	19.3095i	0.450478	−	0.675142i
$819$	49.6503	+	7.71460i	1.73492	+	0.269570i
$820$	1.12104	+	2.69648i	0.0391486	+	0.0941651i
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	0.934621	−	0.355646i	$-0.115739\pi$
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	−0.775309	+	0.631582i	$0.782406\pi$
$822$	36.5493	−	18.0538i	1.27480	−	0.629698i
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	0.505731	−	0.862692i	$-0.331223\pi$
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	−0.494248	+	0.869321i	$0.664556\pi$
$824$	−30.5616	+	10.4411i	−1.06467	+	0.363732i
$825$		−	6.70555i		−	0.233457i
$826$	−7.98985	−	25.4094i	−0.278003	−	0.884106i
$827$		−	23.9044i		−	0.831236i	−0.909539	−	0.415618i	$-0.863565\pi$
$827$		−	23.9044i		−	0.831236i	0.909539	−	0.415618i	$-0.136435\pi$
$828$	25.3152	+	19.3725i	0.879763	+	0.673243i
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.969951	−	0.243301i	$-0.0782303\pi$
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.274271	+	0.961653i	$0.411564\pi$
$830$	−6.83774	−	13.8428i	−0.237341	−	0.480490i
$831$	−20.3800	−	35.2992i	−0.706974	−	1.22452i
$832$	9.61631	−	23.4755i	0.333386	−	0.813866i
$833$	7.31833	−	22.9814i	0.253565	−	0.796259i
$834$	−26.4434	−	17.6439i	−0.915659	−	0.610959i
$835$	−10.1737	+	5.87381i	−0.352076	+	0.203271i
$836$	−1.18640	+	9.10347i	−0.0410327	+	0.314850i
$837$	−21.9187	+	37.9642i	−0.757620	+	1.31224i
$838$	1.08655	−	16.7451i	0.0375343	−	0.578448i
$839$	−46.4174			−1.60251			−0.801253	−	0.598326i	$-0.795833\pi$
$839$	−46.4174			−1.60251			−0.801253	+	0.598326i	$0.795833\pi$
$840$	−14.4307	−	17.1794i	−0.497906	−	0.592745i
$841$	25.4780			0.878551
$842$	0.947163	−	14.5969i	0.0326414	−	0.503043i
$843$	14.2155	−	24.6219i	0.489607	−	0.848025i
$844$	−0.958861	+	7.35749i	−0.0330054	+	0.253255i
$845$	−2.54974	+	1.47209i	−0.0877136	+	0.0506415i
$846$	43.1651	+	28.8013i	1.48405	+	0.990208i
$847$	2.43641	−	15.6804i	0.0837159	−	0.538786i
$848$	−13.1397	+	13.2085i	−0.451219	+	0.453582i
$849$	−32.3038	−	55.9518i	−1.10866	−	1.92026i
$850$	2.15798	+	4.36877i	0.0740183	+	0.149847i
$851$	25.7996	+	14.8954i	0.884398	+	0.510608i
$852$	−1.01118	−	0.773811i	−0.0346425	−	0.0265103i
$853$		−	10.5928i		−	0.362692i	−0.983419	−	0.181346i	$-0.941955\pi$
$853$		−	10.5928i		−	0.362692i	0.983419	−	0.181346i	$-0.0580454\pi$
$854$	−2.06149	+	9.26471i	−0.0705427	+	0.317032i
$855$		−	12.2913i		−	0.420352i
$856$	−2.38101	−	6.96937i	−0.0813814	−	0.238208i
$857$	−0.245410	−	0.141688i	−0.00838305	−	0.00483996i	0.495803	−	0.868435i	$-0.334874\pi$
$857$	−0.245410	−	0.141688i	−0.00838305	−	0.00483996i	−0.504186	+	0.863595i	$0.668207\pi$
$858$	26.9618	−	13.3180i	0.920461	−	0.454669i
$859$	−4.93861	−	8.55393i	−0.168503	−	0.291856i	0.769391	−	0.638779i	$-0.220560\pi$
$859$	−4.93861	−	8.55393i	−0.168503	−	0.291856i	−0.937894	+	0.346922i	$0.887227\pi$
$860$	7.64517	+	18.3891i	0.260698	+	0.627064i
$861$	4.18236	+	10.8006i	0.142535	+	0.368084i
$862$	23.2787	−	34.8883i	0.792875	−	1.18830i
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.896162	−	0.443728i	$-0.853656\pi$
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.0638012	+	0.997963i	$0.520322\pi$
$864$	−16.1374	+	48.0541i	−0.549006	+	1.63483i
$865$	8.24371	−	14.2785i	0.280295	−	0.485485i
$866$	−41.5057	−	2.69321i	−1.41042	−	0.0915192i
$867$	−15.3759			−0.522195
$868$	−25.1449	+	6.14961i	−0.853473	+	0.208731i
$869$	−1.03151			−0.0349916
$870$	−31.2295	−	2.02642i	−1.05878	−	0.0687020i
$871$	−0.0836685	+	0.144918i	−0.00283500	+	0.00491036i
$872$	−2.13420	−	1.86426i	−0.0722732	−	0.0631319i
$873$	−0.961883	+	0.555343i	−0.0325548	+	0.0187955i
$874$	−4.28733	+	6.42551i	−0.145021	+	0.217346i
$875$	−1.65899	+	2.06101i	−0.0560840	+	0.0696749i
$876$	82.3573	−	34.2396i	2.78260	−	1.15685i
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	−0.984811	−	0.173632i	$-0.944450\pi$
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	0.342036	−	0.939687i	$-0.388884\pi$
$878$	−11.1883	+	5.52652i	−0.377585	+	0.186511i
$879$	75.1666	+	43.3975i	2.53531	+	1.46376i
$880$	−8.64745	−	2.29289i	−0.291506	−	0.0772934i
$881$			27.7529i			0.935019i	0.883988	+	0.467509i	$0.154849\pi$
$881$			27.7529i			0.935019i	−0.883988	+	0.467509i	$0.845151\pi$
$882$	−37.0068	−	46.3186i	−1.24608	−	1.55963i
$883$			44.1707i			1.48646i	0.669034	+	0.743232i	$0.266708\pi$
$883$			44.1707i			1.48646i	−0.669034	+	0.743232i	$0.733292\pi$
$884$	−13.2800	+	17.3537i	−0.446656	+	0.583669i
$885$	18.4836	+	10.6715i	0.621321	+	0.358720i
$886$	−12.2551	−	24.8100i	−0.411717	−	0.833508i
$887$	−10.0638	−	17.4310i	−0.337909	−	0.585275i	0.646130	−	0.763227i	$-0.276386\pi$
$887$	−10.0638	−	17.4310i	−0.337909	−	0.585275i	−0.984039	+	0.177952i	$0.943053\pi$
$888$	−18.3363	+	93.1358i	−0.615326	+	3.12543i
$889$	5.01611	−	6.23167i	0.168235	−	0.209003i
$890$	8.25882	+	5.51057i	0.276836	+	0.184715i
$891$	−17.2385	+	9.95263i	−0.577510	+	0.333426i
$892$	−25.6988	−	3.34919i	−0.860461	−	0.112139i
$893$	−6.28724	+	10.8898i	−0.210394	+	0.364414i
$894$	−1.78493	+	27.5079i	−0.0596968	+	0.920000i
$895$	−9.10959			−0.304500
$896$	−27.0889	+	12.7355i	−0.904976	+	0.425462i
$897$	25.3027			0.844831
$898$	0.459978	−	7.08882i	0.0153497	−	0.236557i
$899$	−18.0537	+	31.2699i	−0.602124	+	1.04291i
$900$	11.8773	+	1.54790i	0.395910	+	0.0515967i
$901$	13.8983	−	8.02418i	0.463019	−	0.267324i
$902$	3.84167	+	2.56329i	0.127913	+	0.0853483i
$903$	28.5224	+	73.6569i	0.949167	+	2.45115i
$904$	−8.11832	+	41.2355i	−0.270011	+	1.37147i
$905$	8.28775	+	14.3548i	0.275494	+	0.477170i
$906$	44.4561	+	90.0000i	1.47696	+	2.99005i
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	0.700126	−	0.714020i	$-0.253127\pi$
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	−0.268296	+	0.963336i	$0.586461\pi$
$908$	−10.8084	+	14.1240i	−0.358690	+	0.468720i
$909$			37.4239i			1.24127i
$910$	−11.5819	−	2.57709i	−0.383936	−	0.0854295i
$911$		−	24.0198i		−	0.795811i	−0.917426	−	0.397906i	$-0.869737\pi$
$911$		−	24.0198i		−	0.795811i	0.917426	−	0.397906i	$-0.130263\pi$
$912$	−23.7909	−	6.30821i	−0.787795	−	0.208886i
$913$	−21.1461	−	12.2087i	−0.699834	−	0.404049i
$914$	35.3063	−	17.4398i	1.16783	−	0.576857i
$915$	−3.80262	−	6.58634i	−0.125711	−	0.217738i
$916$	23.9076	−	9.93946i	0.789931	−	0.328409i
$917$	6.37981	−	41.0597i	0.210680	−	1.35591i
$918$	24.2349	−	36.3214i	0.799871	−	1.19878i
$919$	49.7575	−	28.7275i	1.64135	−	0.947632i	0.660992	−	0.750393i	$-0.270136\pi$
$919$	49.7575	−	28.7275i	1.64135	−	0.947632i	0.980355	−	0.197239i	$-0.0631976\pi$
$920$	−5.66917	−	4.95212i	−0.186907	−	0.163267i
$921$	12.0014	−	20.7870i	0.395459	−	0.684956i
$922$	28.0124	+	1.81767i	0.922541	+	0.0598617i
$923$	−0.673370			−0.0221643
$924$	−34.0637	−	9.93325i	−1.12061	−	0.326780i
$925$	11.1938			0.368049
$926$	−50.3981	−	3.27022i	−1.65618	−	0.107466i
$927$	34.1915	−	59.2214i	1.12300	−	1.94509i
$928$	−13.2919	+	39.5806i	−0.436327	+	1.29930i
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	−0.442172	−	0.896930i	$-0.645792\pi$
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	0.555679	+	0.831397i	$0.312458\pi$
$930$	11.5124	−	17.2539i	0.377507	−	0.565779i
$931$	10.6198	−	9.67552i	0.348049	−	0.317102i
$932$	−11.6827	−	28.1006i	−0.382678	−	0.920466i
$933$	20.6162	+	35.7083i	0.674945	+	1.16904i
$934$	−28.6700	+	14.1617i	−0.938110	+	0.463386i
$935$	6.67369	+	3.85305i	0.218253	+	0.126008i
$936$	17.3658	+	50.8307i	0.567619	+	1.66145i
$937$			43.2204i			1.41195i	0.708237	+	0.705975i	$0.249491\pi$
$937$			43.2204i			1.41195i	−0.708237	+	0.705975i	$0.750509\pi$
$938$	0.188353	−	0.0592267i	0.00614995	−	0.00193382i
$939$		−	31.8878i		−	1.04062i
$940$	−9.73126	−	7.44689i	−0.317399	−	0.242891i
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.0916918	−	0.995787i	$-0.529227\pi$
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.908223	+	0.418486i	$0.862561\pi$
$942$	−14.7078	−	29.7754i	−0.479206	−	0.970136i
$943$	1.94295	+	3.36529i	0.0632712	+	0.109589i
$944$	20.0823	−	20.1874i	0.653622	−	0.657044i
$945$	23.4276	+	3.64015i	0.762099	+	0.118414i
$946$	26.1990	+	17.4809i	0.851802	+	0.568352i
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.990969	−	0.134091i	$-0.957188\pi$
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.379358	+	0.925250i	$0.623855\pi$
$948$	0.357390	−	2.74231i	0.0116075	−	0.0890662i
$949$	23.5840	−	40.8488i	0.765571	−	1.32601i
$950$	−0.187940	+	2.89637i	−0.00609756	+	0.0939708i
$951$	50.9190			1.65116
$952$	25.3897	−	4.49073i	0.822886	−	0.145546i
$953$	−47.5308			−1.53967			−0.769837	−	0.638241i	$-0.779662\pi$
$953$	−47.5308			−1.53967			−0.769837	+	0.638241i	$0.779662\pi$
$954$	2.55440	−	39.3663i	0.0827016	−	1.27453i
$955$	−1.49648	+	2.59197i	−0.0484248	+	0.0838743i
$956$	0.0113339	−	0.0869671i	0.000366566	−	0.00281272i
$957$	−42.8623	+	24.7466i	−1.38554	+	0.799943i
$958$	−10.0746	−	6.72211i	−0.325495	−	0.217182i
$959$	−23.7208	+	9.18550i	−0.765986	+	0.296615i
$960$	9.09185	−	22.1952i	0.293438	−	0.716346i
$961$	3.53423	+	6.12147i	0.114008	+	0.197467i
$962$	22.2321	+	45.0082i	0.716792	+	1.45112i
$963$	13.5050	+	7.79713i	0.435193	+	0.251259i
$964$	−3.65400	−	2.79624i	−0.117688	−	0.0900609i
$965$			14.7088i			0.473494i
$966$	−21.9960	−	20.1870i	−0.707708	−	0.649508i
$967$		−	29.3643i		−	0.944292i	−0.881520	−	0.472146i	$-0.843479\pi$
$967$		−	29.3643i		−	0.944292i	0.881520	−	0.472146i	$-0.156521\pi$
$968$	16.0532	−	5.48442i	0.515970	−	0.176276i
$969$	18.3607	+	10.6005i	0.589829	+	0.340538i
$970$	0.235154	−	0.116156i	0.00755035	−	0.00372955i
$971$	−13.3188	−	23.0688i	−0.427419	−	0.740312i	0.569224	−	0.822183i	$-0.307244\pi$
$971$	−13.3188	−	23.0688i	−0.427419	−	0.740312i	−0.996643	+	0.0818708i	$0.973911\pi$
$972$	0.153506	+	0.369231i	0.00492370	+	0.0118431i
$973$	15.4523	+	12.4382i	0.495379	+	0.398749i
$974$	−24.8391	+	37.2269i	−0.795895	+	1.19283i
$975$	8.23364	−	4.75369i	0.263687	−	0.152240i
$976$	−9.79398	+	2.65172i	−0.313498	+	0.0848795i
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	−0.962819	−	0.270146i	$-0.912928\pi$
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	0.715363	+	0.698753i	$0.246261\pi$
$978$	−45.9143	−	2.97928i	−1.46818	−	0.0952668i
$979$	15.7018			0.501832
$980$	8.01224	+	11.4806i	0.255942	+	0.366734i
$981$	6.00019			0.191571
$982$	50.4916	+	3.27629i	1.61125	+	0.104551i
$983$	−22.0131	+	38.1277i	−0.702107	+	1.21609i	0.265618	+	0.964078i	$0.414424\pi$
$983$	−22.0131	+	38.1277i	−0.702107	+	1.21609i	−0.967725	+	0.252007i	$0.918909\pi$
$984$	−8.14565	+	9.32511i	−0.259674	+	0.297274i
$985$	−4.17206	+	2.40874i	−0.132933	+	0.0767489i
$986$	19.9615	−	29.9167i	0.635703	−	0.952743i
$987$	−37.8591	−	30.4743i	−1.20507	−	0.970006i
$988$	−12.0191	+	4.99686i	−0.382378	+	0.158971i
$989$	13.2503	+	22.9502i	0.421336	+	0.729775i
$990$	16.9837	−	8.38923i	0.539778	−	0.266627i
$991$	14.4776	+	8.35865i	0.459896	+	0.265521i	0.712001	−	0.702179i	$-0.247789\pi$
$991$	14.4776	+	8.35865i	0.459896	+	0.265521i	−0.252104	+	0.967700i	$0.581123\pi$
$992$	−18.3141	−	20.7462i	−0.581472	−	0.658692i
$993$			24.9751i			0.792560i
$994$	0.585370	+	0.537230i	0.0185668	+	0.0170399i
$995$			1.27436i			0.0403999i
$996$	39.7839	−	51.9877i	1.26060	−	1.64729i
$997$	23.8844	+	13.7897i	0.756427	+	0.436723i	0.828011	−	0.560711i	$-0.189472\pi$
$997$	23.8844	+	13.7897i	0.756427	+	0.436723i	−0.0715845	+	0.997435i	$0.522806\pi$
$998$	−25.8762	−	52.3856i	−0.819098	−	1.65824i
$999$	−50.1540	−	86.8693i	−1.58680	−	2.74842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.31.8	yes	32
4.3	odd	2	inner	140.2.o.a.31.3	✓	32
5.2	odd	4		700.2.t.c.199.16		32
5.3	odd	4		700.2.t.d.199.1		32
5.4	even	2		700.2.p.c.451.9		32
7.2	even	3		980.2.o.f.411.3		32
7.3	odd	6		980.2.g.a.391.28		32
7.4	even	3		980.2.g.a.391.27		32
7.5	odd	6	inner	140.2.o.a.131.3	yes	32
7.6	odd	2		980.2.o.f.31.8		32
20.3	even	4		700.2.t.d.199.6		32
20.7	even	4		700.2.t.c.199.11		32
20.19	odd	2		700.2.p.c.451.14		32
28.3	even	6		980.2.g.a.391.25		32
28.11	odd	6		980.2.g.a.391.26		32
28.19	even	6	inner	140.2.o.a.131.8	yes	32
28.23	odd	6		980.2.o.f.411.8		32
28.27	even	2		980.2.o.f.31.3		32
35.12	even	12		700.2.t.d.299.6		32
35.19	odd	6		700.2.p.c.551.14		32
35.33	even	12		700.2.t.c.299.11		32
140.19	even	6		700.2.p.c.551.9		32
140.47	odd	12		700.2.t.d.299.1		32
140.103	odd	12		700.2.t.c.299.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	4.3	odd	2	inner
140.2.o.a.31.8	yes	32	1.1	even	1	trivial
140.2.o.a.131.3	yes	32	7.5	odd	6	inner
140.2.o.a.131.8	yes	32	28.19	even	6	inner
700.2.p.c.451.9		32	5.4	even	2
700.2.p.c.451.14		32	20.19	odd	2
700.2.p.c.551.9		32	140.19	even	6
700.2.p.c.551.14		32	35.19	odd	6
700.2.t.c.199.11		32	20.7	even	4
700.2.t.c.199.16		32	5.2	odd	4
700.2.t.c.299.11		32	35.33	even	12
700.2.t.c.299.16		32	140.103	odd	12
700.2.t.d.199.1		32	5.3	odd	4
700.2.t.d.199.6		32	20.3	even	4
700.2.t.d.299.1		32	140.47	odd	12
700.2.t.d.299.6		32	35.12	even	12
980.2.g.a.391.25		32	28.3	even	6
980.2.g.a.391.26		32	28.11	odd	6
980.2.g.a.391.27		32	7.4	even	3
980.2.g.a.391.28		32	7.3	odd	6
980.2.o.f.31.3		32	28.27	even	2
980.2.o.f.31.8		32	7.6	odd	2
980.2.o.f.411.3		32	7.2	even	3
980.2.o.f.411.8		32	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0915727 - 1.41125i) q^{2} +(1.49907 - 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +O(q^{10})\)	\(q+(0.0915727 - 1.41125i) q^{2} +(1.49907 - 2.59647i) q^{3} +(-1.98323 - 0.258463i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(-0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(0.626319 + 1.26796i) q^{10} +(1.93693 + 1.11828i) q^{11} +(-3.64409 + 4.76194i) q^{12} +3.17109i q^{13} +(2.52997 - 2.75667i) q^{14} +2.99814i q^{15} +(3.86639 + 1.02518i) q^{16} +(-2.98390 - 1.72275i) q^{17} +(-7.59365 + 3.75094i) q^{18} +(-1.02618 - 1.77739i) q^{19} +(1.84676 - 0.767779i) q^{20} +(7.39711 - 2.86441i) q^{21} +(1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(6.38656 + 5.57878i) q^{24} +(0.500000 - 0.866025i) q^{25} +(4.47519 + 0.290385i) q^{26} -8.96105 q^{27} +(-3.65867 - 3.82285i) q^{28} -7.38092 q^{29} +(4.23112 + 0.274548i) q^{30} +(2.44599 - 4.23658i) q^{31} +(1.80084 - 5.36255i) q^{32} +(5.80718 - 3.35278i) q^{33} +(-2.70447 + 4.05325i) q^{34} +(-2.61438 - 0.406219i) q^{35} +(4.59812 + 11.0600i) q^{36} +(5.59689 + 9.69410i) q^{37} +(-2.60230 + 1.28543i) q^{38} +(8.23364 + 4.75369i) q^{39} +(-0.914412 - 2.67654i) q^{40} +1.46011i q^{41} +(-3.36501 - 10.7014i) q^{42} +9.95752i q^{43} +(-3.55233 - 2.71844i) q^{44} +(5.18651 + 2.99443i) q^{45} +(-1.66686 - 3.37451i) q^{46} +(-3.06343 - 5.30601i) q^{47} +(8.45786 - 8.50215i) q^{48} +(1.49553 + 6.83838i) q^{49} +(-1.17639 - 0.784927i) q^{50} +(-8.94615 + 5.16506i) q^{51} +(0.819610 - 6.28900i) q^{52} +(-2.32888 + 4.03374i) q^{53} +(-0.820587 + 12.6462i) q^{54} -2.23657 q^{55} +(-5.73001 + 4.81321i) q^{56} -6.15325 q^{57} +(-0.675891 + 10.4163i) q^{58} +(3.55938 - 6.16503i) q^{59} +(0.774910 - 5.94600i) q^{60} +(-2.19681 + 1.26833i) q^{61} +(-5.75488 - 3.83985i) q^{62} +(2.43279 - 15.6572i) q^{63} +(-7.40297 - 3.03249i) q^{64} +(-1.58555 - 2.74625i) q^{65} +(-4.19981 - 8.50238i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(5.47248 + 4.18784i) q^{68} -7.97917i q^{69} +(-0.812681 + 3.65233i) q^{70} +0.212347i q^{71} +(16.0294 - 5.47629i) q^{72} +(-12.8816 - 7.43720i) q^{73} +(14.1933 - 7.01088i) q^{74} +(-1.49907 - 2.59647i) q^{75} +(1.57575 + 3.79020i) q^{76} +(2.13680 + 5.51813i) q^{77} +(7.46261 - 11.1844i) q^{78} +(-0.399413 + 0.230601i) q^{79} +(-3.86099 + 1.04536i) q^{80} +(-4.44995 + 7.70755i) q^{81} +(2.06058 + 0.133707i) q^{82} -10.9174 q^{83} +(-15.4105 + 3.76890i) q^{84} +3.44551 q^{85} +(14.0525 + 0.911837i) q^{86} +(-11.0645 + 19.1643i) q^{87} +(-4.16168 + 4.76428i) q^{88} +(6.07992 - 3.51024i) q^{89} +(4.70082 - 7.04523i) q^{90} +(-5.26080 + 6.53565i) q^{91} +(-4.91490 + 2.04334i) q^{92} +(-7.33344 - 12.7019i) q^{93} +(-7.76862 + 3.83736i) q^{94} +(1.77739 + 1.02618i) q^{95} +(-11.2241 - 12.7147i) q^{96} -0.185459i q^{97} +(9.78758 - 1.48435i) q^{98} -13.3945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

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